From figure,

Radius of cylinder = radius of sphere = r

Height of cylinder = Diameter of sphere = 2r

(i) By formula,

Surface area of sphere = 4πr²

Hence, surface area of sphere = 4πr².

(ii) By formula,

Curved surface area of cylinder = 2πrh

= 2πr × 2r

= 4πr².

Hence, curved surface area of cylinder = 4πr².

(iii) Ratio = $\dfrac{\text{Surface area of sphere}}{\text{C.S.A. of cylinder}} = \dfrac{4πr^2}{4πr^2} = \dfrac{1}{1}$.

Hence, the ratio between these two surface area is 1 : 1.

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CBSE Class IX | Academic Year 2026-2027

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Surface Areas and Volumes — Interactive Study Guide

Formula Master Table

Solid	CSA	TSA	Volume
Cube (a)	4a²	6a²	a³
Cuboid (l,b,h)	2h(l+b)	2(lb+bh+hl)	lbh
Cylinder (r,h)	2πrh	2πr(r+h)	πr²h
Cone (r,h,l)	πrl	πr(l+r)	⅓πr²h
Sphere (r)	4πr²		&frac43;πr³
Hemisphere (r)	2πr²	3πr²	⅔πr³

Common Traps

Cone CSA uses slant height l, NOT height h! l = √(r²+h²)

Hemisphere TSA = CSA + base circle = 2πr² + πr² = 3πr²

Use radius, not diameter! If diameter is given, divide by 2 first.

Quick Self-Check

1. Volume of cube with side 5 cm? (125 cm³)
2. CSA of cylinder with r=7, h=10? (2×22/7×7×10 = 440 cm²)
3. Volume of cone with r=3, h=4? (⅓×π×9×4 = 12π cm³)