Question

find the leight of a cyclinder whose radius is 7 cm and total surface are is 968 cm also find the volume
​

Answer 1

Answer:

Height of the cylinder is 15 cm and the volume of the cylinder is 2310 cm³.

Step-by-step explanation:

Given :-

• Radius of the cylinder = 7 cm
• TSA (Total surface area) of the cylinder = 968 cm².

To find :-

• Height and volume of the cylinder.

Solution :-

★Formula used :

${\boxed{\sf{TSA\:of\: cylinder=2\pi\:r(h+r)}}}$

• Radius = 7 cm

TSA of the cylinder,

= 2πr(h+r)

= [2× (22/7) × 7 (h+7) ] cm²

= [44(h+7)] cm²

According to the question,

44(h+7) = 968

→ h + 7 = 22

→ h = 22-7

→ h = 15

Height of the cylinder is 15 cm.

★Formula used :

${\boxed{\sf{Volume\:of\: cylinder=\pi\:r^2h}}}$

Then,

Volume of cylinder,

= πr²h

= [(22/7) × 7 × 7 × 15 ] cm³

= (22×7×15) cm³

= 2310 cm³

Therefore, the volume of the cylinder is 2310 cm³.

Answer 2

Question:

Find the height of a cyclinder whose radius is 7 cm and total surface area is 968 cm also find the volume.

Solution:

${\underline {\underline {\boxed {\rm {\blue { Given: } }}}}}$

• Base radius of the cylinder = 7cm

• TSA ( Total surface area) = 968cm²

${\underline {\underline {\boxed {\rm {\blue { To \: find: } }}}}}$

• Height of the cylinder

• Volume of the cylinder

${\underline {\underline {\boxed {\rm {\blue { Calculation: } }}}}}$

Let's take height as h

We know,

${\underline {\underline {\boxed {\rm {\orange { TSA\: of \: cylinder = 2πr(h + r) sq \: units} }}}}}$

Substituting values to find height-

$\sf { 968cm²= 2 \times \frac{22}{7} \times7 (h + 7) cm² }$

$\sf { 968cm² = 2 \times \frac{22}{\cancel7} \times \cancel7(h + 7)cm² }$

$\sf { 968cm² = 44(h+7)cm² }$

$\sf { h + 7 = \frac{\cancel{968}}{\cancel{44}} = 22}$

$\sf { h = 22-7}$

$\sf\green { h = 15cm }$

Therefore, height of the cylinder is 15cm.

_____...

Now we have to find volume of the cylinder,

We know,

${\underline {\underline {\boxed {\rm {\orange { Volume\: of \: cylinder = ( πr²h)cubic \: units} }}}}}$

Substituting values to find the volume of the cylinder-

$\sf { Volume \: of \: cylinder = \frac{22}{7} \times 7 \times 7 \times 15 }$

$\sf { Volume \: of \: cylinder = \frac{22}{\cancel7} \times \cancel7 \times 7 \times 15 }$

$\sf { Volume \: of \: cylinder = 22 \times 7 \times 15 }$

$\sf { Volume \: of \: cylinder = 154 \times 15 }$

$\sf { Volume \: of \: cylinder = {2310cm}^{3} }$

Therefore, volume of the cylinder is 2310 cm³.

Required Answers:

• Height of the cylinder= 15cm

• Volume of the cylinder= 2310 cm³.