Question

The radius of the cylinder whose TSA is 2508cm² is 7cm. Find the Volume and Curved surface area of the cylinder. ​

Answer 1

Step-by-step explanation:

Given:-

• Radius of the cylinder = 7cm.

• Total surface area (TSA) of the cylinder = 2508cm².

To Find:-

• The volume of the cylinder.

• The Curved surface area (CSA) of the cylinder.

Solution:-

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

$\sf \implies 2 \pi r( h + r) = 2508$

$\sf \implies 2 \times \dfrac{22}{7} \times 7 \times ( h + 7) = 2508$

$\sf \implies 2 \times 22 ( h + 7) = 2508$

$\sf \implies 44 ( h + 7) = 2508$

$\sf \implies( h + 7) = \dfrac{2508}{44}$

$\sf \implies h + 7 = 57$

$\sf \implies h = 50$

$\sf \therefore \underline{\:\:\underline{\: Height \: of \: the \: cylinder \: (h) = 50cm\:}\:\:}$

$\sf Volume \: of \: the \: cylinder = \pi r^2 h$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \dfrac{22}{7} \times 7 \times 7 \times 50$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 22\times 7 \times 50$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =7700cm^3$

$\underline{\boxed{\sf \therefore Volume \: of \: the \: cylinder = 7700cm^3}}$

$\sf CSA \: of \: the \: cylinder = 2\pi rh$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times \dfrac{22}{7} \times 7 \times 50$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 22 \times 50$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2200cm^2$

$\underline{\boxed{\sf \therefore CSA \: of \: the \: cylinder = 2200cm^2}}$

Answer 2

$\huge\bold{\mathbb{QUESTION}}$

The radius of the cylinder whose TSA is $2508\:cm^2$ is $7\:cm.$ Find the Volume and Curved surface area of the cylinder.

$\huge\bold{\mathbb{GIVEN}}$

• TSA of the cylinder $=2508\:cm^2$

• Radius $=7\:cm.$

$\huge\bold{\mathbb{TO\: FIND}}$

• Volume of the cylinder.

• CSA of the cylinder.

$\huge\bold{\mathbb{SOLUTION}}$

Let the height be $h\:cm.$

We know that:

• $\boxed{\large\sf{TSA_{(Cylinder)} = 2 \pi r(h+r)\:unit^2}}$

Let's find out the height.

Putting the formula.

$2 \pi r(h+r)=2508$

$\implies 2\times {\dfrac{22}{7}}\times 7(h+7)=2508$

$\implies 2\times {\dfrac{22}{\cancel 7}}\times \cancel 7(h+7)=2508$

$\implies 2\times 22(h+7) = 2508$

$\implies 44(h+7) = 2508$

$\implies h+7 = {\dfrac{2508}{44}}$

$\implies h+7 = \cancel{\dfrac{2508}{44}}$

$\implies h+7 = 57$

$\implies h = 57-7$

$\implies {\boxed{\red{h = 50}}}$

So, height $= h\:cm = 50\:cm$

$\:$

We know that:

• $\boxed{\large\sf{Volume_{(Cylinder)} = \pi r^2h\:unit^3}}$

Let's find out the volume.

Putting the formula.

$\{\pi \times(7)^2\times 50\}\:cm^3$

$\implies ({\dfrac{22}{7}}\times7\times7\times 50)\:cm^3$

$\implies ({\dfrac{22}{\cancel7}}\times\cancel7\times7\times 50)\:cm^3$

$\implies (22\times7\times 50)\:cm^3$

$\implies {\boxed{\red{7700\:cm^3}}}$

So, volume $= 7700\:cm^3$

$\:$

We know that:

• $\boxed{\large\sf{CSA_{(Cylinder)} = 2\pi rh\:unit^2}}$

Let's find out the CSA.

Putting the formula.

$(2\times \pi \times7\times50)\:cm^2$

$\implies (2\times {\dfrac{22}{7}}\times7\times50)\:cm^2$

$\implies (2\times {\dfrac{22}{\cancel7}}\times \cancel 7\times50)\:cm^2$

$\implies (2\times 22\times50)\:cm^2$

$\implies {\boxed{\red{2200\:cm^2}}}$

So, CSA $= 2200\:cm^2$

$\huge\bold{\mathbb{THEREFORE}}$

• The volume of the cylinder is $7700\:cm^3.$

• The curve surface area of the cylinder is $2200\:cm^2.$

$\huge\bold{\mathbb{WE\:\, MADE\:\,IT\:\,!!}}$