NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.7

NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.7 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.7.

• Surface Areas and Volumes Class 9 Ex 13.1
• Surface Areas and Volumes Class 9 Ex 13.2
• Surface Areas and Volumes Class 9 Ex 13.3
• Surface Areas and Volumes Class 9 Ex 13.4
• Surface Areas and Volumes Class 9 Ex 13.5
• Surface Areas and Volumes Class 9 Ex 13.6
• Surface Areas and Volumes Class 9 Ex 13.7
• Surface Areas and Volumes Class 9 Ex 13.8
• Surface Areas and Volumes Class 9 Ex 13.9

Board	CBSE
Textbook	NCERT
Class	Class 9
Subject	Maths
Chapter	Chapter 13
Chapter Name	Surface Areas and Volumes
Exercise	Ex 13.7
Number of Questions Solved	9
Category	NCERT Solutions

NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.2

Assume π = unless stated otherwise.

Question 1.
Find the volume of the right circular cone with
(i) radius 6 cm, height 7 cm
(ii) radius 3.5 cm, height 12 cm
Solution.
(i) We have, r = 6 cm and h = 7

Question 2.
Find the capacity in liters of a conical vessel with radius 7 cm, slant height 25 cm height 12 cm, slant height 13 cm
(i) radius 7 cm, slant height 25 cm
(ii) height 12 cm, slant height 13 cm
Solution.

Question 3.
The height of a cone is 15 cm. If its volume is 1570 cm³, then find the radius of the base (use, π = 3.14)
Solution.
Let radius of the base be r cm.

Question 4.
If the volume of a right circular cone of height 9 cm is 48 π cm³, then find the diameter of its base.
Solution.
Let r be the radius of the base.
Given, volume of a right circular cone = 48π cm³

Question 5.
A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity (in kilolitres)?
Solution.
Given, diameter of the top of conical pit = 3.5 m

Question 6.
The volume of a right circular cone is 9856 cm³. If the diameter of the base is 28 cm, find
(i) height of the cone
(ii) slant height of the cone
(iii) curved surface area of the cone
Solution.
We have, d = 28 cm
⇒ r = 14 cm
Volume of a right circular cone = 9856 cm³

Question 7.
A right angled Δ ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.
Solution.

On revolving the right angled Δ ABC about the side AB, we get a right circular cone as shown in the adjoining figure, whose radius (r) = 5 cm and height (h) = 12 cm.
∴ Volume of the solid so obtained = πr²h
= x π x 5 x 5 x 12 3
= π x 5 x 5 x 4 = 100π cm³
Hence, the volume of the solid so obtained is 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.

On revolving the right Δ ABC about the side BC(= 5 cm), we get a cone as shown in the § adjoining figure.
Volume of solid so obtained

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 covered by canvas to protect it from rain. Find the area of the canvas required.
Solution.
Given, diameter (d) = 10.5 m, then
Radius (r) = = 5.25 m and height (h) = 3 m

 

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