Question

The volume of a cylinder is 44¶ and height 7cm.find the CSA and TSA

Answer 1

Appropriate Question :

›»› The volume of a cylinder is 448π cm³ and height 7cm.find the CSA and TSA.

Answer :

›»› The curved surface area of the cylinder is 353 cm², and the total surface area of cylinder is 753.28 cm².

Given :

• Volume of a cylinder = 448π cm³.
• Height of a cylinder = 7 cm.

To Find :

• CSA of cylinder = ?
• TSA of cylinder = ?

How to solve?

Here, in this question we have to find the CSA of cylinder and TSA of cylinder. So, firstly we need to find the radius of a cylinder, after that we will find the CSA of cylinder and TSA of cylinder on the basis of conditions given above

To find the radius of a cylinder, we use the formula of volume of cylinder.

Solution :

As we know that

→ Volume of cylinder = πr²h

→ 448π = πr²h

π will be cancel from both sides,

→ 448 = r²h

→ 448 = r² * 7

→ r² = 448/7

→ r² = 64

→ r = √64

→ r = 8

The radius of a cylinder is 8 m.

Now,

As we know that

→ CSA of cylinder = 2πrh

→ CSA of cylinder = 2 * 22/7 * 8 * 7

→ CSA of cylinder = 2 * 22 * 8

→ CSA of cylinder = 44 * 8

→ CSA of cylinder = 352

The CSA of the cylinder is 353 cm².

As we know that

→ TSA of cylinder = 2πr(r + h)

→ TSA of cylinder = 2 * 22/7 * 8(8 + 7)

→ TSA of cylinder = 2 * 22/7 * 8 * 15

→ TSA of cylinder = 2 * 22 * 8 * 2.14

→ TSA of cylinder = 44 * 8 * 2.14

→ TSA of cylinder = 352 * 2.14

→ TSA of cylinder = 753.28

The TSA of the cylinder is 753.28 cm².

Hence, the curved surface area of the cylinder is 353 cm², and the total surface area of cylinder is 753.28 cm².

Answer 2

Answer:

$\huge \bf \: Given$

Volume of cylinder = 448 cm

Height = 7 cm

$\huge \bf \: To \: find$

CSA AND TSA of cuboid

$\huge \bf \: Solution$

So,

For finding CSA and TSA we have to first find the radius.

As we know that

$\sf \: volume \: = \pi \: {r}^{2} h$

$\sf \: 448 = {r}^{2} \times 7$

$\sf \: {r}^{2} = 448 \div 7$

$\sf {r}^{2} = 64$

$\sf \: r \: = \sqrt[]{64}$

$\sf \: r \: = 8 \: cm$

Radius = 8 cm

Now finding CSA of cylinder

$\sf \: CSA\: = 2\pi rh \:$

$\sf \: CSA = \: 2 \times \dfrac{22}{7} \times 8 \times 7$

$\sf \: CSA \: = 2 \times 22 \times 8$

$\sf \: CSA\: of \: cylinder \: = {352 \: cm}^{2}$

CSA of cylinder = 352 cm².

Now,

Finding TSA of cylinder

$\sf \: TSA \: = 2\pi \: r(r + h)$

$\sf \:TSA = 2 \times \dfrac{22}{7} \times 8(8 + 7)$

$\sf \: TSA =2 \times \dfrac{22}{7} \times 8 \times 15$

$\sf \: TSA \: = 2 \times 22 \times 8 \times 2.14$

$\sf \: TSA \: = 352 \times 2.14$

$\sf \: TSA \: = 753.28 {}^{2}$

TSA of cylinder = 753.28 cm².