Question

the volume of a cylinder is 448 Pie cm cube and its height is 7 cm find its lateral surface area and total surface area

Answer 1

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》To find :

Lateral surface area and Total surface area.

》Given :

Volume of cylinder = $448\pi{cm}^{3}$

Height = 7 cm

》Solution :

In order to find the lateral surface area and Total surface area we first need to find the radius of the cylinder.

⟹ $Volume=\pi{r}^{2}h$

⟹ $448\pi=\pi{r}^{2}\times 7$

⟹ $64={r}^{2}$

⟹ $r=8$

So, the radius of the circle is 8 cm.

Now, lateral surface area -

⟹ $2\pi rh$

⟹ $2\times \frac{22}{7}\times 8\times 7$

⟹ $352\:{cm}^{2}$

So, the lateral surface area of cylinder is  $352\:{cm}^{2}$ .

Now, total surface area -

⟹ $2\pi r(r+h)$

⟹ $2\times \frac{22}{7}\times 8(8+7)$

⟹ $754.2\:{cm}^{2}$

So, the total surface area of cylinder is $754.2\:{cm}^{2}$ .

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