Question

Find the height of a cylinder with a radius of 21 cm and a curved surface area of 3960 cm².​​

Answer 1

Required Solution :

Given:

• Base radius of the cylinder (r) = 21 cm

• C.S.A of cylinder = 3960 cm²

To calculate:

• Height of the cylinder (h) = ?

Calculation:

Here, we are given the radius and C.S.A of the cylinder. By making a suitable equation through the formula of C.S.A, we can find its height.

Let the height of the cylinder be h.

As we know that,

★$\boxed{\sf{{C.S.A}_{(Cylinder)}=(2 \pi rh)sq \: units }}$

Substituting values:

→ $\sf {3960 \: {cm}^{2} =(2 \times \dfrac{22}{7} \times 21 \times h) \: {cm}^{2} }$

→ $\sf {3960 \: {cm}^{2} =(2 \times 22 \times 3 \times h) \: {cm}^{2} }$

→ $\sf {3960 \: {cm}^{2} =(44 \times 3 \times h) \: {cm}^{2} }$

→ $\sf {3960 \: {cm}^{2} =(132 \times h) \: {cm}^{2} }$

→ $\sf {3960 \: {cm}^{2} =132h \: {cm}^{2} }$

→ $\sf {\dfrac{3960}{132} cm = h \: cm }$

→ $\sf {\dfrac{1980}{66} cm = h \: cm }$

→ $\sf {\dfrac{990}{33} cm = h \: cm }$

→ $\sf \red {30 cm = h \: cm }$

Hence, height of the cylinder is 30 cm.

_______________________________

More Formulae:

● Volume of the cylinder = πr²h

● C.S.A of the cylinder = 2πrh

● T.S.A of the cylinder = 2πr(h+r)

Answer 2

✓Verified Answer

Required Solution :

Given:

• Base radius of the cylinder (r) = 21 cm

• C.S.A of cylinder = 3960 cm²

To calculate:

• Height of the cylinder (h) = ?

Calculation:

Here, we are given the radius and C.S.A of the cylinder. By making a suitable equation through the formula of C.S.A, we can find its height.

Let the height of the cylinder be h.

As we know that,

★\boxed{\sf{{C.S.A}_{(Cylinder)}=(2 \pi rh)sq \: units }}

C.S.A

(Cylinder)

=(2πrh)squnits

Substituting values:

→ \sf {3960 \: {cm}^{2} =(2 \times \dfrac{22}{7} \times 21 \times h) \: {cm}^{2} }3960cm

2

=(2×

7

22

×21×h)cm

2

→ \sf {3960 \: {cm}^{2} =(2 \times 22 \times 3 \times h) \: {cm}^{2} }3960cm

2

=(2×22×3×h)cm

2

→ \sf {3960 \: {cm}^{2} =(44 \times 3 \times h) \: {cm}^{2} }3960cm

2

=(44×3×h)cm

2

→ \sf {3960 \: {cm}^{2} =(132 \times h) \: {cm}^{2} }3960cm

2

=(132×h)cm

2

→ \sf {3960 \: {cm}^{2} =132h \: {cm}^{2} }3960cm

2

=132hcm

2

→ \sf {\dfrac{3960}{132} cm = h \: cm }

132

3960

cm=hcm

→ \sf {\dfrac{1980}{66} cm = h \: cm }

66

1980

cm=hcm

→ \sf {\dfrac{990}{33} cm = h \: cm }

33

990

cm=hcm

→ \sf \red {30 cm = h \: cm }30cm=hcm

Hence, height of the cylinder is 30 cm.

_______________________________

More Formulae:

● Volume of the cylinder = πr²h

● C.S.A of the cylinder = 2πrh

● T.S.A of the cylinder = 2πr(h+r)