Geometry - Wikitechy https://www.wikitechy.com/interview-questions/category/geometry/ Interview Questions Tue, 07 Sep 2021 05:34:01 +0000 en-US hourly 1 https://wordpress.org/?v=6.9.4 https://www.wikitechy.com/interview-questions/wp-content/uploads/2025/10/cropped-wikitechy-icon-32x32.png Geometry - Wikitechy https://www.wikitechy.com/interview-questions/category/geometry/ 32 32 Which of the following graph indicates the graph of {(sin t, cos t):- π/2 ≤ t ≤ 0} in xy-plane ? https://www.wikitechy.com/interview-questions/geometry/which-of-the-following-graph-indicates-the-graph-of-sin-t-cos-t-%cf%80-2-%e2%89%a4-t-%e2%89%a4-0-in-xy-plane/ https://www.wikitechy.com/interview-questions/geometry/which-of-the-following-graph-indicates-the-graph-of-sin-t-cos-t-%cf%80-2-%e2%89%a4-t-%e2%89%a4-0-in-xy-plane/#respond Tue, 17 Aug 2021 16:13:15 +0000 https://www.wikitechy.com/interview-questions/?p=1818

Which of the following graph indicates the graph of {(sin t, cos t):- π/2 ≤ t ≤ 0} in xy-plane ?

Plane Geometry

A. d

B. c

C. b

D. a

Answer : C. b

Explanation:

    • When t = -90 then (sin t, cos t) = (-1,0)
    • When t=0 then (sin t, cos t) = (0,1)
    Plot above two points in x-y plane.
]]> https://www.wikitechy.com/interview-questions/geometry/which-of-the-following-graph-indicates-the-graph-of-sin-t-cos-t-%cf%80-2-%e2%89%a4-t-%e2%89%a4-0-in-xy-plane/feed/ 0 What is the radius of the circular plate of thickness 1 cm made by melting a sphere of radius 3 cm ? https://www.wikitechy.com/interview-questions/geometry/what-is-the-radius-of-the-circular-plate-of-thickness-1-cm-made-by-melting-a-sphere-of-radius-3-cm/ https://www.wikitechy.com/interview-questions/geometry/what-is-the-radius-of-the-circular-plate-of-thickness-1-cm-made-by-melting-a-sphere-of-radius-3-cm/#respond Tue, 17 Aug 2021 16:11:06 +0000 https://www.wikitechy.com/interview-questions/?p=1817

What is the radius of the circular plate of thickness 1 cm made by melting a sphere of radius 3 cm ?

A. 6 cm

B. 5 cm

C. 4 cm

D. 7 cm

Answer : A. 6 cm

Explanation :

Given that radius of sphere r = 3 cm
Given that thickness of the plate h = 1 cm

Given that a sphere is melt to produce a circular plate.
Since nothing is added or subtraced then volume of sphere and circular plate both will be equal.
Volume of sphere 
Volume of circular plate 
set both volumes equal to each other



36 = r2
6 = r
Hence the radius is 6 cm.

]]> https://www.wikitechy.com/interview-questions/geometry/what-is-the-radius-of-the-circular-plate-of-thickness-1-cm-made-by-melting-a-sphere-of-radius-3-cm/feed/ 0 In triangle PQR, PQ = 6 cm, PR = 8 cm, and QR = 12 cm. Calculate the area of the triangle PQR ? https://www.wikitechy.com/interview-questions/geometry/in-triangle-pqr-pq-6-cm-pr-8-cm-and-qr-12-cm-calculate-the-area-of-the-triangle-pqr/ https://www.wikitechy.com/interview-questions/geometry/in-triangle-pqr-pq-6-cm-pr-8-cm-and-qr-12-cm-calculate-the-area-of-the-triangle-pqr/#respond Tue, 17 Aug 2021 16:07:57 +0000 https://www.wikitechy.com/interview-questions/?p=1814

In triangle PQR, PQ = 6 cm, PR = 8 cm, and QR = 12 cm. Calculate the area of the triangle PQR ?

A. 23.33 cm2

B. 17.5 cm2

C. 21.33 cm2

D. 28.67 cm2

Answer : C. 21.33 cm2

Explanation:

    • In triangle PQR, by using heron’s formula
    • S = P + Q + R / 2
    • S = 6 + 8 + 12 / 2
    • = 26 / 2 = 13
    • S = 13
    • Area of the triangle PQR = sqrt ( S (S – P) * (S – Q) * (S – R) )
    • = sqrt ( 13 (13 – 6) * (13 – 8) * (13 – 12) )
    • = sqrt ( 455 )
    • Area of the triangle PQR =

21.33 cm2

]]> https://www.wikitechy.com/interview-questions/geometry/in-triangle-pqr-pq-6-cm-pr-8-cm-and-qr-12-cm-calculate-the-area-of-the-triangle-pqr/feed/ 0 If the perimeter and the diagonal of a rectangle is 18 cm and √41 cm respectively.Calculate the area of the rectangular field ? https://www.wikitechy.com/interview-questions/geometry/if-the-perimeter-and-the-diagonal-of-a-rectangle-is-18-cm-and-%e2%88%9a41-cm-respectively-calculate-the-area-of-the-rectangular-field/ https://www.wikitechy.com/interview-questions/geometry/if-the-perimeter-and-the-diagonal-of-a-rectangle-is-18-cm-and-%e2%88%9a41-cm-respectively-calculate-the-area-of-the-rectangular-field/#respond Tue, 17 Aug 2021 16:04:28 +0000 https://www.wikitechy.com/interview-questions/?p=1813

If the perimeter and the diagonal of a rectangle is 18 cm and √41 cm respectively. Calculate the area of the rectangular field ?

A. 25 cm2

B. 29 cm2

C. 18 cm2

D. 20 cm2

Answer : D. 20 cm2

Explanation:

Perimeter of rectangle = 18 cm
2 ( l + b ) = 18 cm
l + b = 18 / 2
= 9 cm
l + b = 9 cm

Diagonal of rectangle = √41 cm
We know that, Diagonal of rectangle = √ [ ( length )2 + ( breadth )2 ] √( l2 + b2) = √41
l2 + b2 = ( √41 )2
l2 + b2 = 41
l2 + b2 + 2 lb – 2 lb = 41
( l + b )2 – 2 lb = 41

Since , we have l + b = 9 , so now
( 9 )2 – 2 l b = 41
81 – 2 lb = 41
2 lb = 81 – 41
2 lb = 40
lb = 40 / 2 = 20 cm 2
l × b = 20 cm2
Therefore, area of rectangular field = 20 cm2

]]> https://www.wikitechy.com/interview-questions/geometry/if-the-perimeter-and-the-diagonal-of-a-rectangle-is-18-cm-and-%e2%88%9a41-cm-respectively-calculate-the-area-of-the-rectangular-field/feed/ 0 Find the area of Rhombus one of whose diagonals measures 8 cm and the other 10 cm ? https://www.wikitechy.com/interview-questions/geometry/find-the-area-of-rhombus-one-of-whose-diagonals-measures-8-cm-and-the-other-10-cm/ https://www.wikitechy.com/interview-questions/geometry/find-the-area-of-rhombus-one-of-whose-diagonals-measures-8-cm-and-the-other-10-cm/#respond Tue, 17 Aug 2021 16:01:16 +0000 https://www.wikitechy.com/interview-questions/?p=1812

Find the area of Rhombus one of whose diagonals measures 8 cm and the other 10 cm ?

A. 47 cm2

B. 34 cm2

C. 40 cm2

D. 64 cm2

Answer : C. 40 cm2

Explanation 1:

Area of triangle formula = 1/2*(base)*(height)
Area of one triangle = 1/2 * (4) * (5)
= 10 cm2.

Total area of rhombus = 4 * area of one triangle
= 4 * 10
= 40 cm2

Explanation 2:

Area of a rhombus is = 1/2 * (length of one diagonal) * (length of another diagonal)
= 1/2 * 8 * 10 cm2
= 40 cm2

]]> https://www.wikitechy.com/interview-questions/geometry/find-the-area-of-rhombus-one-of-whose-diagonals-measures-8-cm-and-the-other-10-cm/feed/ 0 Determine the metal required to make a 21 m long pipe if its inner and outer diameter is 12 m and 10 m respectively ? https://www.wikitechy.com/interview-questions/geometry/determine-the-metal-required-to-make-a-21-m-long-pipe-if-its-inner-and-outer-diameter-is-12-m-and-10-m-respectively/ https://www.wikitechy.com/interview-questions/geometry/determine-the-metal-required-to-make-a-21-m-long-pipe-if-its-inner-and-outer-diameter-is-12-m-and-10-m-respectively/#respond Tue, 17 Aug 2021 15:58:43 +0000 https://www.wikitechy.com/interview-questions/?p=1811

Determine the metal required to make a 21 m long pipe if its inner and outer diameter is 12 m and 10 m respectively ?

A. 725 m3

B. 2534 m3

C. 2843 m3

D. 2647 m3

Answer : A. 725 m3

Explanation:

Find the volume with diameter = 12 m

Radius = Diameter ÷ 2
Radius = 12 ÷ 2 = 6 m
Volume = π * r2 * h
Volume = π * (6)2 * 21
V1 = 2,375 m3

Find the volume with diameter = 10 m

Radius = Diameter ÷ 2
Radius = 10 ÷ 2 = 5 m
Volume = π * r2 * h
Volume = π * (5)2 * 21
V2 = 1650 m3

Find the volume of the metal used:

Volume = V1 – V2
= 2,375 – 1650
Volume = 725 m3

]]> https://www.wikitechy.com/interview-questions/geometry/determine-the-metal-required-to-make-a-21-m-long-pipe-if-its-inner-and-outer-diameter-is-12-m-and-10-m-respectively/feed/ 0 An oblong piece of ground measures 19m 2.5dm by 12m 5dm.From center of each side of the ground, a path 2m wide goesacross to the center of the opposite side.What is the area of the path ? https://www.wikitechy.com/interview-questions/geometry/an-oblong-piece-of-ground-measures-19m-2-5dm-by-12m-5dm-from-center-of-each-side-of-the-ground-a-path-2m-wide-goesacross-to-the-center-of-the-opposite-side-what-is-the-area-of-the-path/ https://www.wikitechy.com/interview-questions/geometry/an-oblong-piece-of-ground-measures-19m-2-5dm-by-12m-5dm-from-center-of-each-side-of-the-ground-a-path-2m-wide-goesacross-to-the-center-of-the-opposite-side-what-is-the-area-of-the-path/#respond Tue, 17 Aug 2021 15:43:50 +0000 https://www.wikitechy.com/interview-questions/?p=1810

An oblong piece of ground measures 19m 2.5dm by 12m 5dm.From center of each side of the ground, a path 2m wide goesacross to the center of the opposite side.What is the area of the path ?

A. 59.5 m2

B. 54 m2

C. 78.54 m2

D. 34 m2

Answer : C. 78.54 m2

Explanation:

Area of path horizontal = 20 * 192.5
= 3850 dm2
Area of path vertical = 20 * 125
= 2500 dm2
Since center path is covered twice so total area,
= (3850 + 2500) – (20 * 20)
= 5950 dm2
Total cost = 1.32 * 59.5 m2
= 78.54 m2

]]> https://www.wikitechy.com/interview-questions/geometry/an-oblong-piece-of-ground-measures-19m-2-5dm-by-12m-5dm-from-center-of-each-side-of-the-ground-a-path-2m-wide-goesacross-to-the-center-of-the-opposite-side-what-is-the-area-of-the-path/feed/ 0 A square field of area 31684 m2 is to be enclosed with the wireplaced at height 1 m, 2 m, 3 m, 4 m above the ground. What length of the wire will be required if its length required for each circuit is 5% greater than the perimeter of the field ? https://www.wikitechy.com/interview-questions/geometry/a-square-field-of-area-31684-m2-is-to-be-enclosed-with-the-wireplaced-at-height-1-m-2-m-3-m-4-m-above-the-ground-what-length-of-the-wire-will-be-required-if-its-length-required-for-each-circuit-is/ https://www.wikitechy.com/interview-questions/geometry/a-square-field-of-area-31684-m2-is-to-be-enclosed-with-the-wireplaced-at-height-1-m-2-m-3-m-4-m-above-the-ground-what-length-of-the-wire-will-be-required-if-its-length-required-for-each-circuit-is/#respond Tue, 17 Aug 2021 15:42:03 +0000 https://www.wikitechy.com/interview-questions/?p=1809

A square field of area 31684 m2 is to be enclosed with the wireplaced at height 1 m, 2 m, 3 m, 4 m above the ground. What length of the wire will be required if its length required for each circuit is 5% greater than the perimeter of the field ?

A. 6456 m

B. 27666 m

C. 2990.4 m

D. 14

Answer : C. 2990.4 m

Explanation:

Given that a square field is to be enclosed by four wires at height 1m, 2m, 3m and 4m.

Area of the square field = 31684 m2
Let’s find the perimeter of square

As we know

Area of square = x2
So,
x2 = 31684 m2
Taking square root on both sides
√x2 = √31684 m2
x = 178 m
So, the length of one side of square is x = 178 m

As we know the perimeter of the square is calculated as

P = 4x
P = 4 * 178
P = 712 m

Given that length of wire for each circuit is 5% more than the length of perimeter of square. So,

Length of wire = Length of perimeter  + 5% of Length of perimeter  
l = 712 + 0.05 * 712
l = 712 + 35.6
l = 747.6 m

As we need to enclose the square field by wires four times at different height; therefore,

Total Length of wire = 4l
Total Length of wire = 4 * 747.6
Total Length of wire = 2990.4 m

So, total length of wire is 2990.4 m

]]> https://www.wikitechy.com/interview-questions/geometry/a-square-field-of-area-31684-m2-is-to-be-enclosed-with-the-wireplaced-at-height-1-m-2-m-3-m-4-m-above-the-ground-what-length-of-the-wire-will-be-required-if-its-length-required-for-each-circuit-is/feed/ 0 A rectangular grassy plot is 112 m by 78 m. It has a gravel path 2.5 m m wide all around it on the inside. Find the area of the path ? https://www.wikitechy.com/interview-questions/geometry/a-rectangular-grassy-plot-is-112-m-by-78-m-it-has-a-gravel-path-2-5-m-m-wide-all-around-it-on-the-inside-find-the-area-of-the-path/ https://www.wikitechy.com/interview-questions/geometry/a-rectangular-grassy-plot-is-112-m-by-78-m-it-has-a-gravel-path-2-5-m-m-wide-all-around-it-on-the-inside-find-the-area-of-the-path/#respond Tue, 17 Aug 2021 15:39:25 +0000 https://www.wikitechy.com/interview-questions/?p=1808

A rectangular grassy plot is 112 m by 78 m. It has a gravel path 2.5 m m wide all around it on the inside.Find the area of the path ?

A. 952 m²

B. 925 m²

C. 912 m²

D. 950 m²

Answer : B. 925 m²

Explanation:

Outer length of the grassy plot = 112 m
Outer breadth of the plot = 78 m

Outer area of the plot = 112 x 78
= 8736 sq m
Width of the path = 2.5 m

Inner length of the plot = 112 – (2 x 2.5)
= 107 m
Inner breadth of the plot = 78 – (2 x 2.5)
= 73 m

Inner area of the plot = 107 x 73
= 7811 sq m

Area of the path = Outer area of the plot – inner area of the plot
= 8736 – 7811
= 925 m²

]]> https://www.wikitechy.com/interview-questions/geometry/a-rectangular-grassy-plot-is-112-m-by-78-m-it-has-a-gravel-path-2-5-m-m-wide-all-around-it-on-the-inside-find-the-area-of-the-path/feed/ 0 A polygon has 77 diagonals. Determine the number of sides ? https://www.wikitechy.com/interview-questions/geometry/a-polygon-has-77-diagonals-determine-the-number-of-sides/ https://www.wikitechy.com/interview-questions/geometry/a-polygon-has-77-diagonals-determine-the-number-of-sides/#respond Tue, 17 Aug 2021 15:36:08 +0000 https://www.wikitechy.com/interview-questions/?p=1807

A polygon has 77 diagonals. Determine the number of sides ?

A. 15

B. 12

C. 17

D. 14

Answer : D. 14

Explanation:

    • The formula for the number of diagonals that can be formed in a polygon with n sides is…..
    • n(n – 3)/2 = D, where n = number of sides, D = total number of diagonals in the polygon.
    • n(n – 3)/2 = 77
      • n

    2

    •  – 3n = 154
      • n

    2

    •  – 3n – 154 = 0
      • n

    2

    •  – 14n – 11n – 154 = 0
    • n(n – 14) + 11(n – 14) = 0
    • (n – 14) (n + 11) = 0

n = -11, 14

Reject n=-11 and Accept n=14. Therefore, The number so sides of the polygon is 14.

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