Question

5. Find the volume of a circular cylinder of height 4 cm,
whose curved surface area is 176 sq cm.
​

Answer 1

Question :-

Find the volume of a circular cylinder of height 4 cm,  whose curved surface area is 176cm².

Given :-

☞ Curved surface area of a cylinder = 176cm²

☞ Height = 4cm

To find :-

☞ Volume of the cylinder

In order to find the Volume, we first have to find the value of the radius.

We know that,

Curved Surface Area = $2\pi rh$

• R being radius
• H being height
• $\pi$ being pi

Substituting the values,

$176 = 2\times\pi \times r\times 4$

$176 = 8\times \dfrac{22}{7} \times r$

$176 = \dfrac{176}{7} \times r$

Transposing all the constants to one side,

$\dfrac{176}{\frac{176}{7} } =r$

$176 \times \dfrac{7}{176} = r$

$7 = r$

Now that we know the value of the radius, let us find the volume.

Volume :-

Formula :- $\pi r^{2} h$

substituting the values,

☞ $\dfrac{22}{7} \times 7\times 7\times 4$

☞ $22 \times 7\times 4$

☞ 616cm³

Some more formulas :-

☞ Total surface area of a cylinder = $2\pi rh + 2\pi r^{2} =\geq 2\pi r(h+r)$

☞ Volume of a cube = a³

☞ Volume of a cuboid = Length × Breadth × Height

Hope it helps!

Happy day!