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Mensuration Mathematics - Mensuration

ICSE - STD 10 - Mathematics (ICSE - English Medium). 62 questions in this chapter.

Question types

Mensuration question types

62 questions across 3 question groups — pick any mix to generate a Mathematics paper with step-by-step answer keys.

62
Questions
3
Question groups
5
Question types
Sample Questions

Mensuration questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 2[2 Mark Question Answer]2 Marks
Water flows at the rate of $10 m$ per minute through a cylindrical pipe $5 mm$ of diameter. How much time would it take to fill a conical vessel whose diameter at he surface is $40 cm$ and depth is $24 cm$?
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Q 3[2 Mark Question Answer]2 Marks
A metal container in the form of a cylinder is surmounted by a hemisphere of the same radius. The internal height of the cylinder is $7\  m$ and the internal radius is $3.\ m.$ Calculate: the internal volume of the container in $m^3$.
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Q 6[3 marks sum]3 Marks
A circus tent is cylindrical to a height of $3$ meters and conical above it. If its diameter is $105$ m and the slant height of the conical portion is $53 m$ calculate the length of the canvas which is $5m$ wide to make the required tent.
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Q 7[3 marks sum]3 Marks
A conical tent is accommodate to $11$ persons each person must have $4$ sq. metre of the space on the ground and $20$ cubic metre of air to breath. Find the height of the cone.
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Q 8[3 marks sum]3 Marks
A vessel in the form of an inverted cone is filled with water to the brim: Its height is $20\ cm$ and the diameter is $16.8\ cm.$ Two equal solid cones are dropped in it so that they are fully submerged. As a result, one-third of the water in the original cone overflows. What is the volume of each of the solid cones submerged?
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Q 9[3 marks sum]3 Marks
The radius of two right circular cylinder are in the ratio of $2 : 3$ and their heights are in the ratio of $5: 4$ calculate the ratio of their curved surface areas and also the ratio of their volumes.
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Q 10[3 marks sum]3 Marks
A metallic cylinder has a radius of 3 cm and a height of 5 cm. It is made of metal A. To reduce its weight, a conical hole is drilled in the cylinder, as shown and it is completely filled with a lighter metal B. The conical hole has a radius of $\frac{3}{2}$ cm and its depth is $\frac{8}{9}$ cm. Calculate the ratio of the volume of the metal A to the volume of metal B in the solid.
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Q 12[4 marks sum]4 Marks
An exhibition tent is in the form of a cylinder surmounted by a cone. The height of the tent above the ground is $85$ m and height of the cylindrical part of $50$ m. If the diameter of the base is $168$ m, find the quantity of canvas required to make the tent. Allow $20\%$ extra for fold and for stitching. Give your answer to the nearest $m^2$.
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Q 13[4 marks sum]4 Marks
Water flows through a cylindrical pipe of internal diameter $7 cm$ at $36 km/hr$. Calculate the time in minutes it would take to fill the cylindrical tank, the radius of whose base is $35 cm$, and height is $1 m$.
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Q 14[4 marks sum]4 Marks
A buoy is made in the form of a hemisphere surmounted by a right circular cone whose circular base coincides with the plane surface of the hemisphere. The radius of the base of the cone is $3.5 m$ and its volume is two-third the volume of hemisphere. Calculate the height of the cone and the surface area of the buoy, correct to two decimal places.
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Q 15[4 marks sum]4 Marks
A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of the balls are 1.5 cm and 2 cm. Find the diameter of the third ball.
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