Aptitude · all questions

Mensuration 3d
practice.

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Q61

A solid metallic cuboid of dimensions 18 cm × 36 cm × 72 cm is molted and recast into 8 cubes of the same volume. What is the ratio of the total surface area of the cuboid to the sum of the lateral surface areas of all 8 cubes?

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Q62

The volume of a solid right circular cylinder of height 8 cm is 392π cm³. Its curved surface area (in cm²) is:

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Q63

A right angled sector of radius

r

cm is rolled up into a cone in such a way that the two binding radii are joined together. Then the curved surface area of the cone is

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Q64

If the radius of the base of a right circular cylinder is increased by 20% and the height is decreased by 30%, then what is the percentage increase/decrease in the volume?

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Q65

The length of the largest possible rod that can be placed in a cubical room is 35√3 m. The surface area of the largest possible sphere that fit within the cubical room

(assuming π = \frac{22}{7})

(in sq. m) is

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Q66

A sphere is placed in a cube so that it touches all the faces of the cube. If 'a' is the ratio of the volume of the cube to the volume of the sphere, and 'b' is the ratio of the surface area of the sphere to the surface area of the cube, then the value of ab is:

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Q67

The external and the internal radii of a hollow right circular cylinder of height 15 cm are 6.75 cm and 5.25 cm respectively. If it is melted to form a solid cylinder of height half of the original cylinder, then the radius of the solid cylinder is

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Q68

A 22.5 m high tent is in the shape of a frustum of a cone surmounted by a hemisphere. If the diameters of the upper and the lower circular ends of the frustum are 21 m and 39 m, respectively, then find the area of cloth (in m²) used to make the tent (ignoring the wastage).

(Use π = \frac{22}{7})

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Q69

Assume that a drop of water is spherical and its diameter is one-tenth of a cm. A conical glass has a height equal to the diameter of its rim. If 32,000 drops of water fill the glass completely. Then the height of the glass (in cm) is:

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Q70

The radii of two circular faces of the frustum of a cone of height 21 cm are 3 cm and 2 cm respectively. What is the volume of the frustum of the cone in cm³

(π = \frac{22}{7}) ?

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Q71

A cone-shaped storage tank's height and radius are 9 and 7 feet, respectively. Determine how much liquid the tank can contain. (Take π = 3.14)

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Q72

The areas of three adjacent faces of a cuboidal solid block of wax are 216 cm², 96 cm² and 144 cm². It is melted and 8 cubes of the same size are formed from it. What is the lateral surface area (in cm²) of 3 such cubes?

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Q73

Balls of marbles of diameter 1.4 cm are dropped into a cylindrical beaker containing some water and fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm?

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Q74

A cylindrical vessel with radius 6 cm and height 5 cm is to be made by melting a number of spherical metal balls of diameter 2 cm. The minimum number of balls needed is:

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Q75

2 cm of rain has fallen on a square km of land. Assuming that 50% of the raindrops could have been collected and contained in a pool having a 100 m × 10 m base, by what level would the water level in the pool have increased?

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Q76

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 sphere to the surface area of the larger sphere is

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Q77

Three solid iron cubes of edges 4 cm, 5 cm and 6 cm are melted together to make a new cube. 62 cm³ of the melted material is lost due to improper handling. The area (in cm²) of the whole surface of the newly formed cube is

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Q78

If the radius of a sphere is increased by 2.5 decimetre (dm), then its surface area increases by 110 dm². What is the volume (in dm³) of the sphere?

(take π = \frac{22}{7})

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Q79

Let x cm² be the surface area and y cm³ be the volume of a sphere such that y = 14x. What is the radius (in cm) of the sphere?

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Q80

A conical tent has to accommodate 25 persons. Each person must have 4 m² of space on the ground and 80 m³ of air to breathe. Find the height of the tent.

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