Aptitude · all questions

Mensuration 3d
practice.

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Q121

Open question

The ratio of total surface area and volume of a sphere is 1 : 7. This sphere is melted to form small spheres of equal size. The radius of each small sphere is

\frac{1}{6}

the radius of the large sphere. What is the sum (in cm²) of curved surface areas of small spheres?

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Q122

Open question

The perimeter of the triangular base of a right prism is 15 cm and radius of the in circle of the triangular base is 3 cm. If the volume of the prism be 270 cm³, then the height of the prism is

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Q123

Open question

40 men took a dip in a pool 30 m long and 25 m broad. If the average water displaced by a man is 5 m³, then what will be the rise (in cm) in level of the pool?

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Q124

Open question

The ratio of the of two cones is 5 : 6 and their volumes are in the ratio 8 : 9. The ratio of their height is:

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Q125

Open question

A 15 m deep well with radius 2.8 m is dug and the earth taken out from it is spread evenly to from a platform of breadth 8 m and height 1.5 m. What will be the length of the platform?

(Take π = \frac{22}{7})

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Q126

Open question

A solid cylinder has total surface area of 462 sq. cm. Its curved surface area is one third of the total surface area. Then the radius of the cylinder is

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Q127

Open question

The radius of the base and height of a right circular cone are in the ratio 5 : 12. If the volume of the cone is

314 \frac{2}{7}

cm³, the slant height (in cm) of the cone will be

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Q128

Open question

If the sum of radius and height of a solid cylinder is 20 cm and its total surface area is 880 cm² then its volume is

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Q129

Open question

A right pyramid stands on a square base of diagonal 10√2 cm. If the height of the pyramid is 12 cm, the area (in cm²) of its slant surface is

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Q130

Open question

N solid metallic spherical balls are melted and recast into a cylindrical rod whose radius is 3 times that of a spherical ball and height is 4 times the radius of a spherical ball. The value of N is:

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Q131

Open question

From a solid cylindrical wooden block of height 18 cm and radius 7.5 cm, a conical cavity of the same height and same radius is taken out. What is total surface area (in cm²) of the remaining solid?

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Q132

Open question

The volume of a cylinder is 4312 cm³. Its curved surface area is one-third of its total surface area. Its curved surface area (in cm²) is:

(Take π = \frac{22}{7})

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Q133

Open question

A right triangular pyramid XYZB is cut from cube as shown in figure. The side of cube is 16 cm. X, Y and Z are mid points of the edges of the cube. What is the total surface area (in cm²) of the pyramid?
Mensuration 3D mcq question image

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Q134

Open question

A spherical ball of radius 1 cm is dropped into a conical vessel of radius 3 cm and slant height 6 cm. The volume of water (in cm³), that can just immerse the ball, is

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Q135

Open question

If the radius of the base of a cone is doubled, and the volume of the new cone is three times the volume of the original cone, then what will be the ratio of the height of the original cone to that of the new cone?

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Q136

Open question

The volume of a hemisphere is

2425 \frac{1}{2}

cm³, Find the radius.

(Take π = \frac{22}{7})

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Q137

Open question

The sum of length, breadth and height of a cuboid is 20 cm. If the length of the diagonal is 12 cm, then find the total surface area of cuboid.

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Q138

Open question

If the radii of the circular ends of a frustum which is 45 cm high be 28 cm and 7 cm then the capacity of the bucket in cubic centimetre is.

(Use π = \frac{22}{7})

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Q139

Open question

The length of the side of a cube is 2.8 cm. What is the volume of the largest sphere that can be taken out of the cube?

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Q140

Open question

A cuboid of size 50 cm × 40 cm × 30 cm is cut into 8 identical parts by 3 cuts. What is the total surface area (in cm²) of all the 8 parts?

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Mensuration 3dpractice.

Mensuration 3d
practice.