Aptitude · all questions

Mensuration 3d
practice.

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Q101

The base of a right prism is a quadrilateral ABCD, given that AB = 9 cm, BC = 14 cm, CD = 13 cm, DA = 12 cm and ∠DAB = 90°. If the volume of the prism be 2070 cm³, then the area of the lateral surface is

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Q102

The circumference of the base of a right circular cone is 44 cm and its height is 24 cm. The curved surface area (in cm²) of the cone is:

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Q103

The height of a circular cylinder is increased six times and the base area is decreased to one ninth of its value. The factor by which the lateral surface of the cylinder increases is

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Q104

If a solid cone of volume 27π cm³ is kept inside a hollow cylinder whose radius and height are equal to that of the cone, then the volume of water needed to fill the empty space is

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Q105

The volume of a conical tent is 1232 m³ and the area of its base is 154 sq. m. Find the length of the canvas required to build the tent, if the canvas is 2 m in width.

(Take π = \frac{22}{7})

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Q106

A spherical metallic shell with 6 cm external radius weight 6688 g. What is the thickness of the shell if the density of metal is 10.5 g per cm³?

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Q107

If 3.96 cubic dm of lead is to be drawn into a cylindrical wire of diameter 0.6 cm, then the length of the wire (in metres), is:

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Q108

A right circular cylinder of maximum volume is cut out from a solid wooden cube. The material left is what percent of the volume (nearest to an integer) of the original cube?

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Q109

The radius of a sphere is reduced by 40%. By what percent will its volume decrease?

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Q110

The radius of the base of a right circular cylinder is increased by 20%. By what per cent should its height be reduced so that its volume remains the same as before?

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Q111

An inverted conical shaped vessel is filled with water to its brim. The height of the vessel is 8 cm and radius of the open end is 5 cm. When a few solid spherical metallic balls each of radius

\frac{1}{2}

cm are dropped in the vessel, 25% water is overflowed. The number of balls is:

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Q112

A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm. Find the volume of wooden toy (nearly)?

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Q113

The base of right pyramid is an equilateral triangle, each side of which is 20 cm. Each slant edge is 30 cm. The vertical height (in cm) of the pyramid is:

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Q114

The base, of a right prism is a regular hexagon of side 5 cm. If its height is 12√3 cm, then its volume (in cm³) is:

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Q115

A hemispherical cup of radius 4 cm is filled to the brim with coffee. The coffee is then poured into a vertical cone of radius 8 cm and height 16 cm. The percentage of the volume of the cone that remains empty is:

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Q116

The radius of the base of a cylinder is 14 cm and its volume is 6160 cm³. The curved surface area (in cm²) is:

(π = \frac{22}{7})

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Q117

A solid metallic sphere of radius 15 cm is melted and recast into spherical balls of radius 3 cm each. What is the ratio of the surface area of the original sphere and the sum of the surface areas of all balls?

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Q118

Two solid right cones of equal height and of radii r₁ and r₂ are melted and made to form a solid sphere of radius R. Then the height of the cone is

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Q119

The curved surface area of a right cylinder is 3696 cm². Its height is three times its radius. What is the capacity (in liters) of the cylinder?

(Take π = \frac{22}{7})

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Q120

Water flows into a tank which is 200 m long and 150 m wide through a pipe of cross-section 0.3 m × 0.2 m at 20 km/hour. Then the time (in hours) for the water level in the tank to reach 8 m is

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