Class 10 ICSE Maths Mensuration Important Questions
Mensuration is the branch of geometry that deals with the measurement of area, length, or volume in 2D and 3D shapes. The 2D shapes can be drawn in a plane like square, rectangle, triangle, circle, etc. and 3D shapes cannot be represented in a plane like bricks, ice-cream cones, football, etc.
Q.1 The radius and the height of a cylinder are in the ratio 2:7. If the cylinder is 704 cm3 , find the total surface area of the cylinder.
Solution
Q2 It costs Rs2200 to paint the inner curved surface of a cylindrical tank 10 m deep. If the rate of painting is Rs20 per m 2 , find (i) the inner curved surface area of the tank (ii) the radius of the base (iii) capacity of the tank in kilolitres
Solution
Q3 The difference between the outer and the inner curved surfaces of a cylinder 14 cm long is 88 cm2 . Find the outer and the inner radii of the cylinder, given that the volume of the metal is 176 cm3
Solution
Q4 .A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.
Solution
Q5 The volume of a conical tent is 1232 m3 and the area of the base floor is 154m2 . Calculate the: (i) radius of the floor. (ii) height of the tent. (iii) length of the canvas required to cover this conical tent if its width is 2 m
Solution
Q6
The height of a cone is 40 cm. A small cone is cut off at the top by a plane parallel to its
base. If its volume be 1/64 of the volume of the given cone, at what height 64 above the
base is the section cut?
Solution
Q7
.The hollow sphere, in which a circus motorcyclist performs his stunts, has a diameter of 7
m. Find the surface area available to the motorcyclist for riding.
Solution
Q8
The diameter of the moon is approximately one-fourth of the diameter of the earth. Find
the ratio of their surface areas.
Solution
Q9 A solid sphere and a solid hemisphere have the same total surface areas. Find the ratio of their volumes.
Solution
Q10
The internal and external diameters of a hollow hemispherical vessel are 14cm and 21
cm respectively. The cost of silver plating of 1 cm2
surface area is Rs0.40. Find the total cost
of silver plating the vessel all over.
Solution
Solution
Q11 The diameter of a sphere is decreased by 25%. By what percent does its curved surface area decrease?
Solution
Q12
The adjoining figure shows a medicine capsule, which is in the shape of a cylinder with
two hemispheres stuck to each of its ends. If the length of the capsule is 14 mm and the
diameter of the capsule is 5 mm, find its surface area.
Solution
Q13
.A hemispherical depression is cut out from one face of a cuboidal block such that the
diameter (cm) of the hemisphere is equal to the edge of the cube. Find the surface area of
the remaining solid.
Solution
Q14
From a solid cylinder of height 7 cm and base diameter 12 cm, a conical cavity of same
height and same base radius is hollowed out. Find the total surface area of the remaining
solid
Solution
Q15 .From a cuboidal solid metallic block of dimensions 15 cm x 10 cm x 5 cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block.
Solution
Q16
A hemispherical tank full of water is emptied by a pipe at the rate of 3
litres per
second. How much time will it take to empty half the tank, if it is 3m in diameter?
Solution
Q17
.A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child
reshapes it in the form of a sphere. Find the radius of the sphere
Solution
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