Ncert – Class 10 – Surface Areas and Volumes– Hots Question

Question 1

A wooden toy is shown in the picture. This is a cuboidal wooden block of dimensions 14 cm× 17 cm ×4 cm. On its top there are seven cylindrical hollows for bees to fit in. Each cylindrical hollow is of height 3 cm and radius 2 cm.
Find the volume of wood in the remaining cuboid after carving out seven cylindrical hollows

Solution

volume of wood = Volume of cuboid – 7× volume of cylinders
= 952 cm³-264 cm³

Question 2

A right-circular cylindrical water tanker supplies water to colonies on the outskirts of a city and to nearby villages. Each colony has a cuboidal water tank. In villages, people come with matkas (spherical clay pots) to fill water for their household.
If a tanker supplies water to 3 colonies and then goes to a village where 400 people fill their matkas, roughly how much water is supplied by the tanker in all? Give your answer in m³

Solution

find the volume of one matka as 38,808 cm3
Finds volume of 400 matkas as roughly 16 m3
Finds volume of 3 cuboidal tanks as 42 × 3 = 126 m3
. Finds the volume of water supplied by the tanker by adding (126 + 16) to get the answer as 142m³
.

Question 3

A golf ball is spherical with about 300 to 500 dimples that help increase its
velocity while in play. Golf balls are traditionally white but available in colours
also. In the given figure, a golf ball has diameter 4·2 cm and the surface has 315
dimples (hemi-spherical) of radius 2 mm. Find the total surface area exposed to the surroundings.

Solution

total surface area exposed to the surroundings = total surface area of sphere – 315× CSA of hemisphere = 4 𝜋 ×(42 mm)² – 315 × 2 𝜋 × (2 mm)² = 18216 mm²

Question 4

A cone, a hemisphere and a cylinder stand on equal bases and have the same height what is
the ratio of their volume?

Solution

V of cone:v of the hemisphere:v of the cylinder
= 1/3πr3
:2/3 πr3
: πr3=1:2:3

Question 5

Ramesh has recently built his house and installed a cylindrical water tank.The dimensions of the
tank are as follows: Radius 50 cm and Height 175 cm.If water is filled in the tank at the rate of
11 litres per minute, how long will it take for thetank to be completely filled?

Solution

V of water= πr2
h=22/7 ×1/2×1/2 x 7/4 = 11000/8 lts
Time taken to fill it completely= 11000/8 x 1/11
=125 minutes=2hrs 5mins

Question 6

The area of the base of a rectangular tank is 7200 𝑐𝑚2 and the volume of water contained in it
is 3 𝑚3 . Find the height of water in the tank

Solution

Height=3x100x100x100/72000=416.67cm

Question 7

A child playing with clay forms a spherical ball with a radius of 3 cm. After some time he recasts the same spherical ball into a cylindrical pillar with a radius of 1 cm. Find the height of the new formed pillar. (Use π = 22 7 )

Solution

Volume of Sphere = Volume of Cylinder
Volume of Sphere = 4/3𝜋 𝑟³
Volume of Cylinder = 𝜋 𝑟² ℎ

4/3𝜋 𝑟³ = 𝜋 𝑟²h
h = 36 𝑐m

Question 8

Aakash has decided to build a 25m long, 10m wide and 2m deep swimming
pool on empty land in the backyard of his house which is 30m long and 15m
wide. He wants to put tiles on the bottom and the four walls of the pool, help
Aakash answer the following questions:

(a) What is the total surface area of the pool?
(b) If he plans to cover the bottom and sides of the pool with square tiles
having side 50cm, how many such tiles will be required?
(c) If each tile costs Rs 25.50, how much will be the total cost?

Solution

(a) Total surface area of the pool= Area of four walls + area of base
= 2(I + b)h +lb
= 2(25 + 10)2 + 25 x 10
= 4(35) + 250
= 140 + 250
= 390 m2
(b) If he plans to cover the bottom and sides of the pool with square
tiles having side 50cm, how many such tiles will be required?
Area of one tile = 50 x 50 =2500 cm2 = 0.25cm2
Number of tiles required = 390/0.25 = 1560 tiles
(c) If each tile costs Rs 48.50, how much will be the total cost?
Total cost = 1560 x 48.50 = Rs. 75660

Question 9

A heap of rice is in the form of a cone of base diameter 24 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

Solution

Canvas cloth required to just cover the heap = CSA of conical heap = πrl
= 22/7× 12 × 12.5
= 3300/7 m²
= 471.43 m²

Question 10

A solid wooden toy is in the form of hemisphere surmounted by a cone of same
radius. The radius of hemisphere is 3.5 cm and the total wood used in the
making of toy is 166 5/6
cm³. Find the height of the toy. Also, find the cost of painting the
hemispherical part of the toy at the rate of ₹ 10 per cm². (Use π=22/7)

Solution

the cost of painting the hemispherical part of the toy
= ₹(77 × 10)
= 770