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Mensuration - Volume and Surface Areas

Multiple Choice Questions

31.

If the height of a cylinder is 4 times its circumference, the volume of the cylinder in terms of its circumference c, is

$fraction numerator 2 straight c cubed over denominator straight pi end fraction$
$4 πc cubed$
$straight c cubed over straight pi$
$straight c cubed over straight pi$

455 Views

32.

If the surface area of sphere is 346.5 cm², then its radius [ taking π = 22/7 ] is

7 cm
3.25 cm
5.25 cm
9 cm

262 Views

33.

If each side of a cube is increased by 10% the volume of the cube will increase by

30%
10%
33.1%
33.1%

190 Views

34.
A conical cup is filled with ice cream. The ice-cream forms a hemispherical shape on its open top. The height of the hemispherical part is 7 cm. The radius of the hemispherical part equals the height of the cone. Then the volume of the ice-cream is $open square brackets straight pi space equals space 22 over 7 close square brackets$

1078 cubic cm

1708 cubic cm

7108 cubic cm

7108 cubic cm

1078 cubic cm

Volume of the ice-cream = Volume of hemisphere part + Volume of conical part.
Radius (r) = 7 cm.
Volume of hemisphere =

2 over 3 πr cubed

equals space open parentheses 2 over 3 cross times 22 over 7 cross times 7 cross times 7 close parentheses space cu. space cm.

Volume of conical part =

1 third πr squared straight h

open square brackets because space straight r space equals space straight h close square brackets

equals space open parentheses 1 third cross times 22 over 7 cross times 7 cross times 7 cross times 7 close parentheses space cu. space cm.

∴ Volume of ice-cream

equals space 2 over 3 cross times 22 over 7 cross times 7 cubed space plus space 1 third cross times 22 over 7 cross times 7 cubed equals space 22 over 7 cross times 7 cubed space equals space 22 space cross times space 7 squared equals space 1078 space cu. space cm.

323 Views

35.

A large solid sphere is melted and moulded to form identical right circular cones with base radius and height same as the radius of the sphere. One of these cones is melted and moulded to form a smaller solid sphere. Then the ratio of the surface area of the smaller to the surface area of the larger sphere is

$1 space colon space 3 to the power of 4 over 3 end exponent$
$1 space colon space 2 to the power of 3 over 2 end exponent$
$1 space colon space 3 to the power of 2 over 3 end exponent$
$1 space colon space 3 to the power of 2 over 3 end exponent$

463 Views

36.

A ball of lead 4 cm in diameter is covered with gold. If the volume of the gold and lead are equal, then the thickness of gold [given $cube root of 2 space equals space 1.259$ ] is approximately.

5.038 m
5.190 cm
1.038 cm
1.038 cm

551 Views

37.

The base of a right prism is an equilateral triangle. If the lateral surface area and volume is 120 cm², 40√3 cm³ respectively then the side of base of the prism is

4 cm
5 cm
7 cm
40 cm

849 Views

38.

The base of a right prism is a right angle triangle with two sides 5cm and 12 cm. The height of the prism is 10 cm. The height of the prism is 10 cm. The total surface area of the prism is

360 sq cm
300 sq cm
330 sq cm
325 sq cm

510 Views

39.

The height of the right pyramid whose area of the base is 30m² and volume is 500 m³, is

50 m
60 m
40 m
20 m

238 Views

40.

The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be 1/27 th of the volume of the given cone, at what height above the base is the section made?

19 cm
20 cm
12 cm
15 cm

241 Views