MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.7

MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.7

Assume π = \(\frac{22}{7}\), unless stated otherwise.

Question 1.
Find the volume of the right circular cone with

1. radius 6 cm, height 7 cm
2. radius 3.5 cm, height 12 cm.

Solution:
1. Here, radius of the cone r = 6 cm
height (h) = 7 cm
Volume = \(\frac{1}{3}\) x πr²h
= \(\frac{1}{3}\) x \(\frac{22}{7}\) x 6 x 6 x 7 cm³
= 22 x 2 x 6 cm³
= 264 cm³

2. Here, radius of the cone (r) ;
= 3.5 cm = \(\frac{35}{10}\) cm
Height (h) = 12 m
Volume of the cone

Question 2.
Find the capacity in litres of a conical vessel with

1. radius 7 cm, slant height 25 cm
2. height 12 cm, slant height 13 cm

Solution:
1. Here, r = 7 and l = 25 cm

Thus, the required capacity of the conical vessel is 1.232 l.

2. Here, height (h) – 12 cm and l = 13 cm

Thus, the required capacity of the conical vessel is \(\frac{11}{35}\) l.

Question 3.
The height of a cone is 15 cm. If its volume is 1570 cm³, find the radius of the base. (Use 71 = 3.14)
Solution:
Here, height of the cone (h) = 15 cm
Volume of the cone (v) = 1570 cm³
Let the radius of the base be ‘r’ cm.

Question 4.
If the volume of a right circular cone of height 9 cm is 48 JI cm3, find the diameter of its base.
Solution:
Volume of cone = \(\frac{1}{3}\) πr²h
\(\frac{1}{3}\) x πr² x 9 = 48π
r² = \(\frac{48π}{9π}\) x 3
r² = 16
r = 4 cm
Diameter = 2 x 4 = 8 cm

Question 5.
A conical pit of top diameter 3,5 m is 12 m deep. What is its capacity in kilolitres?
Solution:
d = 3.5 m
r = 1.75 m
h = 12m
Volume of the pit = \(\frac{1}{3}\) x \(\frac{22}{7}\) x 1. 75 x 1.75 x 12
= 38.5 m³ = 38.5 kl (1 kl= 1 m³)

Question 6.
The volume of a right circular cone is 9856 cm³. If the diameter of the base 28 cm, find.

(i) height of the cone.
(ii) slant height of the cone.
(iii) curved surface area of the cone.

Solution:
V = 9856 cm²
d =28 cm
r = 14 cm

Question 7.
A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the sides 12 cm. Find the volume of the solid 30 obtained.
Solution:
h = 12cm
r = 5cm

Volume of solid, V₁ = \(\frac{1}{3}\)πr²h
= \(\frac{1}{3}\) x π x 5 x 5 x 12
= 100π cm³

Question 8.
If the triangle ABC in the Question 7 above is revolved about the side 5 cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.
Solution:
h = 5 cm
r = 12 cm
Volume of solid, V₂ = \(\frac{1}{3}\) x π x 12 x 12 x 5
= 240π

Question 9.
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 by covered canvas to protect it from rain. Find the area of the canvas required.
Solution:
d = 10.5 m ⇒ r = 5.25 m
h = 3m
Volume of heap of wheat = \(\frac{1}{3}\) x \(\frac{22}{7}\) x 5.25 x 5.25 x 3
= 86.625 m³
l² = 3² + (5.25)²
l = \(\sqrt{9+27.56}\) = \(\sqrt{36.56}\) = 6.04 cm
Area of canvas required = CSA of cone –
= \(\frac{22}{7}\) x 5.25 x 6.04 = 99.66 m²

MP Board Class 9th Maths Solutions