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Important questions based on NCERT syllabus for Class 10 Chapter 13 - Surface Areas and Volumes:
Question 1: The decorative block shown in Fig. is made of two solids - a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. (Take π = 22/7)
The total surface area of the cube
= 6×(edge)^2=6×5×5 cm^2 = 150 cm^2.
Note that the part of the cube where the hemisphere is attached is not included in the surface area.
So, the surface area of the block = TSA of cube - base area of hemisphere + CSA of hemisphere
= 150 − πr^2 + 2πr^2
= (150+πr^2) cm,
= 150 cm^2 + (22/7 × 4.2/2 × 4.2/2) cm^2
= (150+13.86) cm^2
= 163.86 cm^2
Question 2: 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.
Volume of cone = 13 × π × 6 × 6 × 24 cm^3
If r is the radius of the sphere, then its volume is 4/3πr^3 .
Since, the volume of clay in the form of the cone and the sphere remains the same, we have
4/3 × π × r^3 = 1/3 × π × 6 × 6 × 24
i.e., r^3 = 3 × 3 × 24 = 3^3 × 2^3
So r = 3 × 2 = 6
Therefore, the radius of the sphere is 6 cm.
Question 3: A hemispherical tank full of water is emptied by a pipe at the rate of 25/7 litres per second. How much time will it take to empty half the tank, if it is 3m in diameter? (Take π = 22/7)
Radius of the hemispherical tank = 32 m
Volume of the tank = 2/3 × 22/7 × (32)3 m^3 = 99/14 m^3
So, the volume of the water to be emptied
= 1/2 × 99/14 m^3 = 99/28 × 1000 litres
= 99000/28 litres
Since, 257 litres of water is emptied in 1 second, 9900028 litres of water will be emptied in 99000/28×725 seconds.
i.e., in 16.5 minutes