1. Find the surface areas and volumes of spheres of the following radii:

(i) 4 cm (π = 3.14)

Solution:

Here, r = 4 cm, S = ?, V = ?

Surface area of a sphere = 4πr²

∴ S = 4 × 3.14 × 4 × 4

∴ S = 200.96 cm²  ... (i)

Volume of a sphere = \(\displaystyle \frac {4}{3}\) πr³

∴ V = \(\displaystyle \frac {4}{3}\) × 3.14 × 4 × 4 × 4

∴ V = 267.9466 ...

∴ V = 267.95 cm³  ... (ii)

1. Find the surface areas and volumes of spheres of the following radii:

(ii) 9 cm (π = 3.14)

Solution:

Here, r = 9 cm, S = ?, V = ?

Surface area of a sphere = 4πr²

∴ S = 4 × 3.14 × 9 × 9

∴ S = 1017.36 cm²  ... (i)

Volume of a sphere = \(\displaystyle \frac {4}{3}\) πr³

∴ V = \(\displaystyle \frac {4}{3}\) × 3.14 × 9 × 9 × 9

∴ V = 3052.08 cm³  ... (ii)

1. Find the surface areas and volumes of spheres of the following radii:

(iii) 3.5 cm (π = 3.14)

Solution:

Here, r = 3.5 cm, S = ?, V = ?

Surface area of a sphere = 4πr²

∴ S = 4 × 3.14 × 3.5 × 3.5

∴ S = 153.86 cm²  ... (i)

Volume of a sphere = \(\displaystyle \frac {4}{3}\) πr³

∴ V = \(\displaystyle \frac {4}{3}\) × 3.14 × 3.5 × 3.5 × 3.5

∴ V = 179.5033 ...

∴ V = 179.50 cm³  ... (ii)

2. If the radius of a solid hemisphere is 5cm, then find its curved surface area and total surface area. (π = 3.14)

Solution:

Here, r = 5 cm, Sc = ?, St = ?

Curved surface area of a hemisphere = 2πr²

∴ Sc = 2 × 3.14 × 5 × 5

∴ Sc = 157 cm²  ... (i)

Total surface area of a hemisphere = 3πr²

∴ St = 3 × 3.14 × 5 × 5

∴ St = 235.5 cm²  ... (ii)

3. If the surface area of a sphere is 2826 cm² then find its volume. (π = 3.14)

Solution:

Here, S = 2826 cm², r = ?, V = ?

Surface area of a sphere = 4πr²

∴ 2826 = 4 × 3.14 × r²

∴ \(\displaystyle \frac {2826}{4 \times 3.14}\) = r²

∴ 225 = r²

∴ \(\displaystyle \sqrt{225}\) = r

∴ 15 = r

i.e. r = 15 cm  ... (i)

Now,

Volume of a sphere = \(\displaystyle \frac {4}{3}\) πr³

∴ V = \(\displaystyle \frac {4}{3}\) × 3.14 × 15 × 15 × 15

∴ V = 14130 cm³  ... (ii)

4. Find the surface area of a sphere, if its volume is 38808 cubic cm. (π = \(\displaystyle \frac {22}{7}\))

Solution:

Here, V = 38808 cm³, r = ?, S = ?

Volume of a sphere = \(\displaystyle \frac {4}{3}\) πr³

∴ 38808 = \(\displaystyle \frac {4}{3}\) × \(\displaystyle \frac {22}{7}\) × r³

∴ \(\displaystyle \frac {38808 \times 3 \times 7}{4 \times 22}\) = r³

∴ 9261 = r³

∴ \(\displaystyle \sqrt[3]{9261}\) = r

∴ 21 = r

i.e. r = 21 cm  ... (i)

Now,

Surface area of a sphere = 4πr²

∴ S = 4 × \(\displaystyle \frac {22}{7}\) × 21 × 21

∴ S = 5544 cm²

5. Volume of a hemisphere is 18000π cubic cm. Find its diameter.

Solution:

Here, V = 18000 cm³, r = ?, d = ?

Volume of a hemisphere = \(\displaystyle \frac {2}{3}\) πr³

∴ 18000 = \(\displaystyle \frac {2}{3}\) × \(\displaystyle \frac {22}{7}\) × r³

∴ \(\displaystyle \frac {18000 \times 3 \times 7}{2 \times 22}\) = r³

∴ 27000 = r³

∴ \(\displaystyle \sqrt[3]{27000}\) = r

∴ 30 = r

i.e. r = 30 cm  ... (i)

Now,

Diameter = 2r

∴ Diameter = 2 × 30

∴ Diameter = 60 cm  ... (ii)

  Lesson 9 : Main Page
Standard 9 : Main Page

This page was last modified on
21 February 2026 at 12:20