Let the radius of the sphere be r.

By formula,

Surface area of the sphere = 4πr²

Substituting values we get :

$\Rightarrow 4πr^2 = 154 \\[1em] \Rightarrow r^2 = \dfrac{154}{4π} \\[1em] \Rightarrow r^2 = \dfrac{154}{4 \times \dfrac{22}{7}} \\[1em] \Rightarrow r^2 = \dfrac{154 \times 7}{4 \times 22} \\[1em] \Rightarrow r^2 = \dfrac{49}{4} \\[1em] \Rightarrow r = \sqrt{\dfrac{49}{4}} \\[1em] \Rightarrow r = \dfrac{7}{2} \text{ cm}.$

By formula,

Volume of a sphere (V) = $\dfrac{4}{3}πr^3$

$V = \dfrac{4}{3} \times \dfrac{22}{7} \times \Big(\dfrac{7}{2}\Big)^3 \\[1em] = \dfrac{4}{3} \times \dfrac{22}{7} \times \dfrac{343}{8} \\[1em] = \dfrac{11}{3} \times 49 \\[1em] = \dfrac{539}{3} \\[1em] = 179 \dfrac{2}{3} \text{ cm}^3$

Hence, volume of the sphere is $179 \dfrac{2}{3} \text{ cm}^3$.

BRIGHT TUTORIALS

CBSE Class IX | Academic Year 2026-2027

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Excellence in Education

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)