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Mensuration 3d
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Q21

A solid metallic cube of side 9 cm and a solid metallic cuboid having dimensions 5 cm, 13 cm, 31 cm are melted to form a single cube. How much (in Rs.) is the cost to polish the new at a rate of Rs. 10 per cm²?

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Q22

A wall 12 m long, 9 m high and 90 cm thick is to be constructed. Given that one pack contains 450 bricks, how many packs of bricks will be required if each brick is of dimensions 10 cm × 7.5 cm × 7 cm and the cement and sand mixture occupies one-eighteenth volume of the wall? (Rounded off to the nearest integer)

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Q23

If a right circular cone is separated into solids of volumes V₁, V₂, V₃ by two planes parallel to the base which also trisect the altitude, then V₁ : V₂ : V₃ is

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Q24

A sector of radius 10.5 cm with the central angle 120° is folded to form a cone by joining the two bounding radii of the sector. What is the volume (in cm³) of the cone so formed?

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Q25

A sphere of diameter 6 cm is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is 12 cm. If the sphere is just completely submerged in water, then the rise of water level in the cylindrical vessel is:

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Q26

A solid cube has side 8 cm. It is cut along diagonals of top face to get 4 equal parts. What is the total surface (in cm²) of each part?

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Q27

The base of a right pyramid is a square of side 8√2 cm and each of its slant edge is of length 10 cm. What is the volume (in cm³) of the pyramid?

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Q28

The base of a solid right prism of height 10 cm is a square and its volume is 160 m³. What is the total surface area of the prism (in cm²)?

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Q29

A solid lead sphere of radius 11 cm is melted and recast into small solid spheres of radius 2 cm each. How many maximum number (in integer) of such spheres can be made?

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Q30

A hemisphere is kept on top of a cube. Its front view is shown in the given figure. The total height of the figure is 21 cm. The ratio of curved surfaces area of hemisphere and total surface area of cube is 11 : 42. What is the total volume (in cm³) of figure?
Mensuration 3D mcq question image

Mensuration 3D mcq question image

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Q31

The height of a solid cylinder in 30 cm and the diameter of its base is 10 cm. Two identical conical holes each of radius 5 cm and height 12 cm are drilled out. What is the surface area (in cm²) of the remaining solid?

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Q32

The internal measure of a cuboidal room are with length as 12 m, breadth as 8 m and height as 10 m. The total cost (in Rs.) of white washing all four walls of the room and also the ceiling of the room, if the cost of white washing is Rs. 25 per m² is:

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Q33

If the radius of a sphere is increased by 4 cm, its surface area is increased by 464π cm². What is the volume (in cm³) of the original sphere?

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Q34

Which of the following two will provide more volume?
I. A cuboid of edges 6 cm, 7 cm and 8 cm
II. A cube of edge 7 cm

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Q35

The curved surface area of a right circular cone is 2310 cm² and its radius is 21 cm. If its radius is increased by 100% and height is reduced by 50%, then its capacity (in litres) will be (correct to one decimal place):

(Take π = \frac{22}{7})

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Q36

A prism has a regular hexagonal base with side 6 cm. If the total surface area of prism is 216√3 cm², then what is the height (in cm) of prism?

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Q37

Water is flowing at the rate of 5 km/h through a pipe of diameter 14 cm into a rectangular tank which is 50 m long 44 m wide. The time taken (in hours) for the rise in the level of water in the tank to be 7 cm is

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Q38

The areas of three adjacent faces of a cuboidal tank are 3 m², 12 m² and 16 m². The capacity of the tank, in litres is:

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Q39

If a cuboid of dimensions 32 cm × 12 cm × 9 cm is cut into two cubes of same size, what will be the ratio of the surface area of the cuboid to the total surface area of the two cubes?

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Q40

A sector is formed by opening out a cone of base radius 8 cm and heigh 6 cm. Then the radius of the sector is (in cm).

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