Question

The area of the base of a right circular cylinder is 15400 cm^2 and its volume is 92400 cm^3. Find its Lateral Surface Area.

Answer 1

Step-by-step explanation:

$area \: of \: circle \: or \: base \: of \: cylinder = \pi \: {r}^{2} \\ \pi \: {r}^{2} = 15400 \\ {r}^{2} = \frac{15400 \times 7}{22} = 4900 \\ r = \sqrt{4900 } = 70cm$

$volume = \pi \: {r}^{2} h \\ \pi \: {r}^{2} h = 92400 \\ \pi \: {70}^{2} h = 92400 \\ h = \frac{92400 \times 7 }{22 \times 70 \times 70} \\ h = 6 {cm}^{2}$

$lateral \: surface \: area \: of \: cylinder = 2\pi \: rh = 2 \times \frac{22}{7} \times 70 \times 6 = 2640 {cm}^{2}$

Answer 2

Answer:

15457.2 cm^2

Step-by-step explanation:

vol. of the cylinder = πr^2h

and, area of the base of cylinder = πr^2

so, we can say that

vol. of the cylinder = area of base × h

given:

vol. of the cylinder = 92400 cm^3

area of base = 15400 cm^2

now,

vol. of cylinder = area of base × h

92400 = 15400 × h

h = 92400/15400

h = 6 cm

and,

area of base = πr^2

15400 = 22/7 × r^2

r^2 = 15400 × 7/22

r^2 = 4900

r = 70 cm

now,

LSA of cylinder = 2πrh

= 2×22/7×70×6

= 2640 cm^2