Question

If the volume of a cylinder of height 7cm is 448¶ cm3,find its lateral surface area and total surface area.

Answer 1

Lsa = 4.4 x 45 sq cm
TSa = (44×45 × 1.15 ) ÷7 sq cm

Answer 2

$\large\underline\pink{Given:-}$

• Total volume of a cylinder is 448π cm³ and height is 7cm.

$\large\underline\pink{To find:-}$

• Fine it's lateral surface area and total surface area ....?

$\large\underline\pink{Solutions:-}$

• Volume of the cylinder = 448 cm³
• height of cylinder = 7cm

Then,

Volume of cylinder = πr²h

$\: \: \: \: \: \leadsto \: \: \pi \: {r}^{2} \: h \: \: = \: \: {448} \pi$

$\: \: \: \: \: \leadsto \: \: {r}^{2} \: \: = \: \: \frac{{448} \pi}{\pi \: \times \: {7}}$

$\: \: \: \: \: \leadsto \: \: {r}^{2} \: \: = \: \: \frac{447}{7}$

$\: \: \: \: \: \leadsto \: \: {r}^{2} \: \: = \: \: {64}$

$\: \: \: \: \: \leadsto \: \: {r} \: \: = \: \: {8}$

Lateral surface area of the cylinder = 2πrh

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: \frac{22}{7} \: \times \: {8} \: \times \: {7}$

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: {22} \: \times \: {8}$

$\: \: \: \: \: \leadsto \: \: {r} \: \: = \: \: {352} \: {cm}^{2}$

Total surface area of cylinder = 2πr(h + r)

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: \frac{22}{7} \: \times \: {8} \: \times \: {({7} \: + \: {8})}$

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: \frac{22}{7} \: \times \: {8} \: \times \: {15}$

$\: \: \: \: \: \leadsto \: \: \frac{5280}{7}$

$\: \: \: \: \: \leadsto \: \: {754.286} \: {cm}^{2}$

Hence, The lateral surface area and total surface area is 354cm² and 754.286cm²

$\large\underline\pink{More \: Information:-}$

• Volume of cylinder ( Area of base × height ).

= (πr²) × h

= πr²h

• Curved surface = ( Perimeter of base ) × height.

= (2πr) × h

= 2πrh

• Total surface are = Area of circular ends + curved surface area.

= 2πr² + 2πrh

= 2πr(r + h)

• Where, r = radius of the circular base of the cylinder.
• h = height of cylinder.