Question

$\large\underline{ \sf Question :-}$
⠀
The curved surface area of a cylinder is 176 cm² and its area of the base is 38.5 cm². Find the volume of the cylinder. (Take π = 22/7) ​

Answer 1

Answer:

Given :-

• The curved surface area of a cylinder is 176 cm² and its area of the base is 38.5 cm².

To Find :-

• What is the volume of the cylinder.

Solution :-

First, we have to find the radius of a cylinder :

Given :

• Area of the base = 38.5 cm²

According to the question by using the formula we get,

$\bigstar \: \: \sf\boxed{\bold{Area\: of\: Base_{(Cylinder)} =\: {\pi}r^2}}\: \: \: \bigstar$

where,

• π = Pie or 22/7
• r = Radius

So,

$\implies \bf Area\: of\: Base_{(Cylinder)} =\: {\pi}r^2$

$\implies \sf 38.5 =\: \dfrac{22}{7} \times r^2$

$\implies \sf 38.5 \times \dfrac{7}{22} =\: r^2$

$\implies \sf \dfrac{269.5}{22} =\: r^2$

$\implies \sf 12.25 =\: r^2$

$\implies \sf \sqrt{12.25} =\: r$

$\implies \sf 3.5 =\: r$

$\implies \sf\bold{r =\: 3.5\: cm}$

Hence, the radius of a cylinder is 3.5 cm .

Now, we have to find the height of a cylinder :

Given :

• CSA of Cylinder = 176 cm²
• Radius = 3.5 cm

According to the question by using the formula we get,

$\bigstar \: \: \sf\boxed{\bold{C.S.A._{(Cylinder)} =\: 2{\pi}rh}}\: \: \: \bigstar$

where,

• π = Pie or 22/7
• r = Radius
• h = Height

So,

$\implies \bf C.S.A._{(Cylinder)} =\: 2{\pi}rh$

$\implies \sf 176 =\: 2 \times \dfrac{22}{7} \times 3.5 \times h$

$\implies \sf 176 =\: \dfrac{44}{7} \times 3.5 \times h$

$\implies \sf 176 =\: \dfrac{154}{7} \times h$

$\implies \sf 176 \times \dfrac{7}{154} =\: h$

$\implies \sf \dfrac{1232}{154} =\: h$

$\implies \sf 8 =\: h$

$\implies \sf\bold{h =\: 8\: cm}$

Hence, the height of a cylinder is 8 cm .

Now, we have to find the volume of a cylinder :

Given :

• Radius = 3.5 cm
• Height = 8 cm

According to the question by using the formula we get,

$\bigstar \: \: \sf\boxed{\bold{Volume_{(Cylinder)} =\: {\pi}r^2h}}\: \: \: \bigstar$

So,

$\dashrightarrow \bf Volume_{(Cylinder)} =\: {\pi}r^2h$

$\dashrightarrow \sf Volume_{(Cylinder)} =\: \dfrac{22}{7} \times (3.5)^2 \times 8$

$\dashrightarrow \sf Volume_{(Cylinder)} =\: \dfrac{22}{7} \times (3.5 \times 3.5) \times 8$

$\dashrightarrow \sf Volume_{(Cylinder)} =\: \dfrac{22}{7} \times 12.25 \times 8$

$\dashrightarrow \sf Volume_{(Cylinder)} =\: \dfrac{22}{7} \times 98$

$\dashrightarrow \sf Volume_{(Cylinder)} =\: \dfrac{2156}{7}$

$\dashrightarrow \sf Volume_{(Cylinder)} =\: 308\: cm^2$

$\sf\bold{\underline{\therefore\: The\: volume\: of\: the\: cylinder\: is\: 308\: cm^2\: .}}$