Surface Areas Cylinder & Sphere | Exercise 13.4 | Q9

CBSE Class 9 Maths | NCERT Solution to Exercise

Question 9: A right circular cylinder just encloses a sphere of radius r. Find

(i) surface area of the sphere
(ii) curved surface area of the cylinder,
(iii) ratio of the areas obtained in (i) and (ii)

NCERT Solution to Class 10 Maths

Explanatory Answer | Exercise 13.4 Question 9

Part (i): Surface Area of Sphere

Given Data: Radius of the sphere = r
Surface area of sphere = 4 × π × r2

Part (ii): Curved Surface Area of Cylinder

Height of the cylinder, h = Diameter of the sphere = 2r
Radius of the cylinder = Radius of the sphere = r
Curved Surface area (CSA) of a cylinder = 2 × π × r × h
= 2 × π × r × (2r)
= 4 × π × r2

Part (iii): Ratio of the CSA of Cylinder to CSA of Sphere

Ratio = $\frac{\text{Surface Area of Sphere}}{\text{Surface Area of Cylinder}}$
= $\frac{4 × π × r^2 }{ 4 × π × r^2 }$ = 1
Ratio of their surface areas = 1 : 1

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NCERT Solutions for Class 9 Math | Chapter 13 Video Solutions

Exercise 13.4 | Surface Area of Spheres & Hemispheres

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