Mensuration
1. Find the diagonal of cuboid if length,
breadth and height are 5, 9 and 8cm.
(a) 170
(b) √170
(c) √160
(d) 150
2. Area of three adjacent surfaces of cuboid
are 56cm2, 72cm2 and 63cm2 , then find its
volume ?
(a) 405
(b) 540
(c) 504
(d) 450
3. If diagonal of a cube is 6cm, then find its
total surface area ?
(a) 62
(b) 52
(c) 72
(d) 82
4. If three cubes of side 3cm each have been
kept in a line touching each other then, find
the lateral surface area of such figure ?
(a) 27
(b) 73
(c) 72
(d) 29
5. The ratio of volume of two cubes are 8 : 9,
then find the ratio of their surface area ?
(a)
(b) √3
(c) √3
(d)
(a) 5748
(c) 5479
(b) 5749
(d) 5478
9. Three metallic blocks are melt to form a
cube, if the length, breadth and height of three
blocks are 9, 4 and 16, then find the lateral
surface area of cube ?
(a) 567
(b) 576
(c) 756
(d) 567
10. Radius and height of a right circular
cylinder is 4 and 14cm, then find its volume ?
(a) 704
(b) 740
(c) 470
(d) 407
11. Radius of a right circular cone is 4cm, then
find the ratio of its volume and curved surface
area. If height is 3cm ?
(a) 4 : 3
(b) 5 : 7
(c) 3 : 7
(d) 4 : 5
12. Radius of sphere is increased by 15%, then
what will be the increment in its surface area ?
(a) 32.25
(b) 30
(c) 45
(d) 35.75
√
6. The ratio of sides of any cuboid is 2 : 1 : 3
and its volume is 48cm3, then find its diagonal
?
(a) 2
(b) √14
(c) 2√14
(d) 7
7. Find the curved surface area of sphere
having diameter 14cm.
(a) 606
(b) 616
(c) 605
(d) 615
8. Total surfaces area of a hemisphere is
1848cm, then find its volume ?
13. A cube has been inscribed in a sphere, find
the volume of the portion excluded from the
cube ?
(a)
√
(c) 2
(b)
√
1
(d)
(√
)
√
√
14. If diameter and height of cone is 30cm and
8cm, then find its lateral surface area ?
(a) 108
(b) 801
(c) 810
(d) 180
15. Find the volume of the cone, if the height
and radius are 14 and 3cm ?
(a) 123
(b) 132
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Mensuration
(c) 231
(d) 213
16. Ratio of volumes of two cones is 1 : 4 and
the ratio of their height is 25 : 64, then find the
ratio of their diameters ?
(a) 5 : 6
(b) 4 : 7
(c) 3 : 5
(d) 4 : 5
23. 10cm of height bucket is in form of
frustum. The radius of its base and top are 7
and 14cm, then find its volume ?
(a) 703
(b) 730
(c) 370
(d) 730
17. A sphere is cut from a hemisphere, find the
ratio of volume of hemisphere and sphere ?
(a) 4 : 1
(b) 3 : 2
(c) 4 : 7
(d) 5 : 9
24. Base radius of a cylinder is increased by 5%
and its height is decreased by 5% , then find
the effect on its curved surface area ?
(a) 0.25% increase (b) 0.25%decrease
(c) 5% increase
(d) 5% decrease
18. Height of a prism is 5cm and its base is an
equilateral triangle with side 2cm, then find its
volume ?
(a) 5√3
(b) 5√7
(c) 5√11
(d) 5√17
25. Find the slant height of regular tetrahedron
of side 2√ cm
(a) 2
(b) 3
(c) 2√3
(d) 9
19. Perimeter of base of a prism is 30cm and its
sides are in ratio 5 : 12 : 13 the height of the
prism is 10cm, then find its volume ?
(a) 200
(b) 300
(c) 400
(d) 500
26. Find the area of the shaded portion of an
equilateral triangle ?
r
r
a
r
20. Ratio of radius and height of a right circular
cone is 4 : 3 and its volume is 96 cm3, then
what will be its slant height ?
(a) 5(6)
(b) 5(6)
(c) 5(6)
(d) 5(6)
21. If radius is doubled and height is also
doubled, then what will be effect on volume of
a right circular cone ?
(a) 700 increase
(b) 800% increase
(c) 600 increase
(d) 400 increase
22. Find curved surface area of a cylindrical
shell, if sum of its outer & inner radius is 7cm
and its height is 5cm ?
(a) 202
(b) 220
(c) 250
(d) 270
a
r
a
(a) r2
(b)
(c)
(d)
27. Find the area of sector having 7cm arc and
2cm radius ?
(a) 14
(b) 28
(c) 7
(d)
28. Find the area of a triangle having sides 4cm
and 7cm with the angle between these side 30°
?
(a) 28
(b) 14
(c) 7
(d)
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Mensuration
29. Find the area of equilateral triangle having
height 13√ cm ?
(a) 169
(b) 169√3
(c) 196
(d) 196√3
30. From the figure, ABC is a right angled
triangle and BD is drawn from B point to
hypotenuse AC, BD ⊥ AC. If BD and AC are 4cm
and 6cm, then find the area of ABC.
35. Side of a square is decreased by 12% , then
find its effect on its area ?
(a) 22.56
(c) 25.75
(b) 21.5
(d) 27.25
36. Find the area of a triangle having sides
12cm, 13cm and 15cm ?
(a) 20√14
(b) 14√20
(c) 5√20
(d) 7√14
A
37. A square is drawn on a diagonal of a
square, then find the ratio of their area ?
(a) 1 : 3
(b) 1 : √2
(c) 1 : 4
(d) 1 : 2
D
B
(a) 10
(c) 12
C
(b) 8
(d) 6
31. If hypotenuse of an isosceles right angled
triangle is 3√ cm, then find its area ?
(a) 9
(b)
(c) 7
(d) 8
32. Diameter of a wheel is 7cm, how many
revolution it will take to cover a distance of 5.5
km ?
(a) 250
(b) 2500
(c) 25000
(d) 25
33. Outer and inner circumference of a ring are
150 and 120cm, then find its width ?
(a) 4.7
(b) 5.2
(c) 6.5
(d) 7.1
34. Find the area of square having diagonal
4cm ?
(a) 4
(b) 6
(c) 8
(d) 12
38. A circle is inscribed inside a square and
another circle is circumscribed around that
square, then find the ratio of area of these
circles ?
(a) 1 :
(b) 1 : 2
(c) : 2
(d) 1 : √2
39. Adjacent sides of a parallelogram are 12cm
and 16cm, the perpendicular on the smaller
side is 8cm, then find the perpendicular on the
larger side ?
(a) 2
(b) 4
(c) 6
(d) 8
40. Find the area of shaded portion, if the side
of square is a cm.
(a)
(b)
(c)
(d)
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Mensuration
41. Find the area of hexagon of side 16cm ?
(a) 384
(c) 384√6
(b) 382
(d) 384√3
42. Length of perpendicular drawn on each
side of equilateral triangle from any point
inside it are 2√3, 5√3 and 7√3 cms. Then find
the area of the triangle ?
(a) 196√3
(b) 169√3
(c) 196
(d) 169
47. The ratio of area of an equilateral triangle
to that of its circumcircle is ?
(a)
√
(b)
√
(c)
√
(d)
√
48. If four circles of equal radius are inscribed
in a square of side 4a, then find the area of
shaded region ?
43. A calf has been tide with 6cm long row, if
the length of row is taken 22cm, then what
extra area it will graze ?
(a) 448
(b) 484
(c) 844
(d) 848
44. If the area and circumference of a circle
are equal, then find the area of the circle ?
(a) 2
(b) 4
(c) 6
(d) 8
45. One side of a right angled triangle is 63cm
difference of other side and hypotenuse is
21cm, then find the length of the hypotenuse ?
(a) 105
(b) 106
(c) 109
(d) 501
46. Find the area of shaded region, if radius of
semicircle is a cm.
4a
(a)
(b) 24a2
(c)
(d)
49. Find the area of a ring between two
concentric circles whose circumferences are
176cm and 264cm ?
(a) 3081
(b) 3091
(c) 8031
(d) 3080
50. Perimeter of a triangle is 72cm and its sides
are in the ratio 3 : 5 : 4, then find the area of
the triangle ?
(a) 126
(b) 216
(c) 363
(d) 493
a
O
(a)
(c)
(
1)
(b)
(d)
(
)
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