Aptitude · all questions

Mensuration 3d
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Q1

The radius and height of a right circular cone are in the ratio 3 : 4. If its curved surface area (in cm²) is 240π. Then its volume (in cm³) is:

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Q2

A cylindrical pencil of diameter 1.2 cm has one of its end sharpened into a conical shape of height 1.4 cm. The volume of the material removed is

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Q3

A sphere and a hemisphere have the same volume. The ratio of their curved surface area is:

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Q4

A tank 40 m long, 30 m broad and 12 m deep is dug in a field 1000 m long and 30 m wide. By how much will the level of the field rise if the earth dug out of the tank is evenly spread over the field?

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Q5

A tank is in the form of a cuboid with length 12 m. If 18 kilolitre of water is removed from it, the water level goes down by 30 cm. What is the width (in m) of the tank?

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Q6

A solid brass sphere of radius 2.1 dm is converted into a right circular cylindrical rod of length 7 cm. The ratio of total surface areas of the rod to the sphere is

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Q7

A solid cylinder has radius of base 14 cm and height 15 cm. 4 identical cylinders are cut from each base as shown in the given figure. Height of small cylinder is 5 cm. What is the total surface area (in cm²) of the remaining part?
Mensuration 3D mcq question image

Mensuration 3D mcq question image

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Q8

A cylindrical vessel whose base is horizontal and is of internal radius 3.5 cm contains sufficient water so that when a solid sphere is placed inside, water just covers the sphere. The sphere fits in the Cylinder exactly. The depth of water in the vessel before the sphere was put, is

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Q9

A hemispherical depression of diameter 4 cm is cut out from each face of a cubical block of sides 10 cm. Find the surface area of the remaining solid (in cm²).

(Use π = \frac{22}{7})

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Q10

The lateral surface area of frustum of a right circular cone if the area of its base is 16π cm² and the diameter of circular upper surface is 4 cm and slant height 6 cm, will be

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Q11

A semi-circular sheet of metal of diameter 28 cm is bent into an open conical cup. The depth of the cup is approximately

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Q12

A hemispherical tank full of water is emptied by a pipe at the rate of 7.7 litres per second. How much time (in hours) will it take to empty

\frac{2}{3}

part of the tank, if the internal radius of the tank is 10.5 m?

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Q13

The base of a cone and a cylinder have the same radius 6 cm. They have also the same height 8 cm. The ratio of the curved surface of the cylinder to that of the cone is

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Q14

The curved surface area of a cylindrical pillar is 264 m² and its volume is 924 m³

(Taking π = \frac{22}{7}) .

Find the ratio of its diameter to its height

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Q15

A solid has 12 vertices and 30 edges. How many faces does it have?

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Q16

The diameter of a 120 cm long roller is 84 cm. It takes 500 complete revolutions of the roller to level a ground. The cost of levelling the ground at Rs. 1.50 sq. m. is:

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Q17

A cuboidal shaped water tank, 2.1 m long and 1.5 m broad is half filled with water. If 630 litres more water is poured into tank, the water level will rise

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Q18

The radii of two circular faces of the frustum of a cone of height 10.5 cm are 5 cm and 3 cm respectively. What is its volume in cm³

(π = \frac{22}{7}) ?

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Q19

The radius of a cylinder is increased by 120% and its height is decreased by 40%. What is the percentage increase in its volume?

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Q20

The radius of two circular cylinders are in the ratio 3 : 2 and the ratio of their volumes is 27 : 16. What is the ratio of their heights?

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