Question

The difference between the inner and outer surface areas of a cylindrical pipe is 88 cm. If the height of
hechiedecal pipe is 14 cm and volume is 175 cm .find the inner and outer radu of the pipe​

Answer 1

Step-by-step explanation:

curved surface area of cylinder = 2πrh

let the radius of outer surface be r1

let the radius of inner surface be r2

height of the pipe = 14 cm

difference between the outer and inner surface area = 88

$2\pi \: r1h - 2\pi \: r2h = 88 \\ 2\pi \: h(r1 - r2) = 88 \\2 \times \frac{22}{7} \times 14(r1 - r2) = 88 \\ 2 \times 22 \times 2 \times (r1 - r2) = 88 \\ r1 - r2 = \frac{88}{22 \times 4} \\ r1 - r2 = 1$

volume of cylinder = πr2^2h = 175

$\frac{22}{7} \times {(r2)}^{2} \times 14 = 175 \\ {(r2)}^{2} = \frac{175}{22 \times 2} \\ {(r2)}^{2} = \frac{175}{44} \\ r2 = \sqrt{ \frac{175}{44} } \\ r2 = { \sqrt{3.9}} \\ approx \: \sqrt{4} = 2$

substitute r2 in r1 - r2 = 1

$r1 - 2 = 1 \\ r1 = 1 + 2 \\ r1 = 3$

therefore the outer radius = 3 cm

inner radius = 2 cm

hope you get your answer