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
Exercise: 13.4 Question 9 Cylinder
(i) surface area of the sphere
(ii) curved surface area of the cylinder,
(iii) ratio of the areas obtained in (i) and (ii)


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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

 


NCERT Solutions for Class 9 Math | Chapter 13 Video Solutions



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