Question

. If the volume of a cylinder is 448 πсmcube and
its height is 7 cm, find its lateral and total
surface area.​

Answer 1

Your answer is given below =》》

Given :

Volume of the cylinder is 448π cm³,

height of the cylinder is 7 cm.

Let the radius be r cm.

We know that,

Volume of cylinder = πr²h

=> 448π = πr²h

=>

= r² × 7

=> 448 = r² × 7

=>

= r²

=> 64 = r²

=>

=r

=> 8 = r

Therefore,

the radius of the cylinder is 8 cm.

:

Lateral surface area and total surface area of the cylinder.

= 2πrh

= 2 × × 8 × 7

= 352 cm²

.

= 2πr(r + h)

= 2 × × 8 ( 8 + 7)

= 754.28 cm²

Answer 2

Answer:

The Total surface area is 754.28 cm² and Lateral surface area is 352 cm².

Step-by-step explanation:

Volume of the cylinder is 448π cm³,

Height of the cylinder is 7 cm.

Let the radius be r cm.

★ Volume of cylinder = πr²h

⇒ 448π = πr²h

⇒ $\sf{\dfrac{448\pi}{\pi}}$ = r² × 7

⇒ 448 = r² × 7

⇒ $\sf{\dfrac{448}{7}}$ = r²

⇒ 64 = r²

⇒ $\sf{\sqrt{64}}$ = r

⇒ 8 = r

The radius of the cylinder is 8 cm.

★ Lateral surface area -

⇒ LSA = 2πrh

⇒ 2 × $\sf{\frac{22}{7}}$ × 8 × 7

⇒ 352 cm²

★ Total Surface Area -

⇒ TSA = 2πr(r + h)

⇒ 2 × $\sf{\dfrac{22}{7}}$ × 8 ( 8 + 7)

⇒ 754.28 cm²

Therefore, the Total surface area is 754.28 cm² and Lateral surface area is 352 cm².