Question

The TSA of a cylinder is 6512 cm^2 and circumference of its base is 88 cm. Find the Volume of the Cylinder

Answer 1

Answer:

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Answer 2

Solution :

$\underline{\bf{Given\::}}}$

The total surface area of a cylinder is 6512 cm² & circumference of it's base is 88 cm.

$\underline{\bf{Explanation\::}}}$

As we know that circumference (perimeter) of circle = 2πr so;

$\mapsto\sf{2\pi r=88}\\\\\mapsto\sf{2\times 22/7 \times r=88}\\\\\mapsto\sf{44/7 \times r=88}\\\\\mapsto\sf{r=\cancel{88} \times 7/\cancel{44}}\\\\\mapsto\sf{r=2\times 7}\\\\\mapsto\bf{r=14\:cm}$

Now;

Using formula of the TSA of a cylinder :

$\boxed{\bf{TSA =2\pi r(r+h)}}}}$

$\mapsto\sf{2\pi r(r+h) = 6512}\\\\\mapsto\sf{2\times 22/7 \times 14 (14+h) = 6512}\\\\\mapsto\sf{44/\cancel{7} \times \cancel{14} (14 + h) = 6512}\\\\\mapsto\sf{44 \times 2(14 +h) = 6512}\\\\\mapsto\sf{88 \times (14+h) = 6512}\\\\\mapsto\sf{1232 + 88h = 6512}\\\\\mapsto\sf{88h = 6512 - 1232}\\\\\mapsto\sf{88h = 5280}\\\\\mapsto\sf{h=\cancel{5280/88}}\\\\\mapsto\bf{h=60\:cm}$

As we know that volume of the cylinder :

$\boxed{\bf{Volume=\pi r^{2} h\:\:\:\:(cubic\:unit)}}}}$

$\longrightarrow\sf{Volume\:_{(cylinder)}= \pi r^{2} h }\\\\\longrightarrow\sf{Volume\:_{(cylinder)}= 22/7 \times (14)^{2} \times 60 }\\\\\longrightarrow\sf{Volume\:_{(cylinder)}= 22/\cancel{7} \times \cancel{14} \times 14 \times 60 }\\\\\longrightarrow\sf{Volume\:_{(cylinder)}= 22 \times 2\times 14 \times 60 }\\\\\longrightarrow\bf{Volume\:_{(cylinder)}= 36960\:cm^{3}}$

Thus;

The volume of the cylinder will be 36960 cm³ .