Question

The volume of a sphere 36πcm'3 ,then find the total surface area of the sphere

Answer 1

Solution

Give:-

• Volume of sphere = 36π cm³

Find:-

• Surface area of sphere .

Explanation

Using Formula

☛ Volume of sphere = 4/3. π.r³

☛ Surface area of sphere = 4.π.r²

So,

➠ Volume of sphere = 36 π

➠ 36 π = 4/3.π.r³

➠ r³ = 36 × 3/4

➠r³ = 9 × 3

➠ r³ = 3 × 3 × 3

➠ r = (3 × 3 × 3)^(1/3)

➠ r = 3^(3×1/3)

➠ r = 3 .

Now,

➠ Surface area of sphere = 4.π.r²

➠ Surface area of sphere = 4.π.(3)²

➠ Surface area of sphere = 4 × 9 × π

➠ Surface area of sphere = 36 π cm².

Hence

• Surface area of sphere = 36π cm²

Answer 2

➬ TSA of sphere = 113.14 cm²

Step-by-step explanation:

Given:

• Volume of sphere is 36π cm³.

To Find:

• What is the total surface area of the sphere ?

Solution: We know that the volume of sphere

➬ Volume of sphere = 4/3πr³ cubic units

But 4/3πr³ = 36π cm³

$\implies{\rm }$ r³ = 36π x 3/4π

$\implies{\rm }$ r³ = 9 x 3

$\implies{\rm }$ r³ = 27

$\implies{\rm }$ r = ³√3 x 3 x 3

$\implies{\rm }$ r = 3 cm

Hence, the radius of sphere is 3 cm.

★ Total Surface Area of sphere = 4πr² ★

$\implies{\rm }$ TSA of sphere = 4 x 22/7 x (3)² cm²

$\implies{\rm }$ 88/7 x 9 cm²

$\implies{\rm }$ 792/7 cm²

$\implies{\rm }$ 113.14 cm²

Hence, the surface area of sphere is 113.14 cm².