Question

If the curved surface area of a right circular cylinder is 704 sq.cm, and height is 8 cm, find the volume of the cylinder​

Answer 1

Given :-

CSA of cylinder =  704 cm²

Height = 8 cm

To Find :-

Volume

Solution :-

We know that

CSA of cylinder = 2πrh

704 = 2 × 22/7 × r × 8

704 = 44/7 × r × 8

704 × 7/44 × 8 = r

14 = r

Now

Volume = πr²h

Volume = 22/7 × (14)² × 8

Volume = 22/7 × 196 × 8

Volume = 22 × 28 × 8

Volume = 4928 cm³

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

Curved Surface Area of Cylinder = 704 sq. cm

and

Height of cylinder, h = 8 cm

Let assume that the radius of cylinder be r cm

We know,

Curved Surface Area of cylinder is

$\boxed{ \tt{ \: CSA_{cylinder} \: = \: 2 \: \pi \: r \: h \: }}$

where,

• CSA is Curved Surface Area

• h is height

• r is radius.

So, on substituting the values, we get

$\rm :\longmapsto\:704 = 2 \times \dfrac{22}{7} \times r \times 8$

$\rm :\longmapsto\:32 = 2 \times \dfrac{1}{7} \times r \times 8$

$\rm :\longmapsto\:2 = \dfrac{1}{7} \times r$

$\rm \implies\:\boxed{ \tt{ \: r \: = \: 14 \: cm \: }}$

Now, we know that,

$\boxed{ \tt{ \: Volume_{cylinder} \: = \: \pi \: {r}^{2} \: h \: \: }}$

So, on substituting the values, we get

$\rm :\longmapsto\: \: Volume_{cylinder} \: = \: \dfrac{22}{7} \: \times {(14)}^{2} \times \: 8\: \:$

$\rm :\longmapsto\: \: Volume_{cylinder} \: = \: \dfrac{22}{7} \: \times 14 \times 14\times \: 8\: \:$

$\rm :\longmapsto\: \: Volume_{cylinder} \: = \: 22 \times 2 \times 14\times \: 8\: \:$

$\rm :\longmapsto\: \: Volume_{cylinder} \: = \: 44 \times 112\: \:$

$\rm :\longmapsto\: \boxed{ \tt{ \: \: Volume_{cylinder} \: = \: 4928 \: {cm}^{3} \: \: }}$

More to know :-

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²