Question

The sum of the radius of the base and height of a cylinder is 37 M if the total surface area of the solid cylinder is 1628m square find the volume of the cylinder

Answer 1

Here's the answer

Let 'r' and 'h' be the radius and height of the solid cylinder respectively.

Given, r + h = 37 cm    

Total surface area of the cylinder = 1628 cm2.. Given

∴ 2 πr (r + h) = 1628 cm2

➡️ 2 πr × 37 cm = 1628 cm2

$\sf{ 2 × 22/7 × r × 37 = 1528 cm {}^{2} }$

$\sf{r = \frac{1628 \times 7}{2 \times 22 \times 37}}$

$\sf{r = 7 \: cm}$

r + h  = 37 cm 

➡️ 7 + h = 37

➡️ h = 37 – 7

➡️ 30 cm

$\sf{Volum e \: \: of \: \: cylinder = \pi \: r {}^{2} h}$

$\sf{ = \frac{22}{7} \times {7}^{2} \times 30}$

$\sf{ = \frac{22}{7} \times 7 \times 7 \times 30}$

$\sf{ = 22 \times 7 \times 30}$

$\sf{ = 4620 \: cm {}^{3}}$

Hence,

Volume of cylinder = 4620 cu.cm.

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Thanks !