Question

The difference between the outer and inners surfaces of a right circular metallic pipe is 176cm^2. If the pipe is made of 396cm^2 metal, the sum of outer and inner radii (in cm) is (Take π=22/7)
a) 5
b) 6
c) 5.5
d) 4.5

Answer 1

Given :- The difference between the outer and inners surfaces of a right circular metallic pipe of length 14cm is 176cm^2. If the pipe is made of 396cm^3 metal, the sum of outer and inner radii (in cm) is (Take π=22/7)

a) 5

b) 6

c) 5.5

d) 4.5

Solution :-

Let outer radius is R cm and inner radius is r cm.

Than,

→ Difference between Outer surface area - inner surface area = 176cm².

→ 2πRh - 2πrh = 176

→ 2 * (22/7) * 14 * [ R - r ] = 176

→ 88 * (R - r) = 176

dividing both sides by 88,

→ (R - r) = 2 cm. --------- Eqn.(1)

Now,

→ The volume of metal used is = 396cm³ .

→ External volume − internal volume = 396 cm³.

→ πR²h - πr²h = 396

→ πh(R² - r²) = 396

using (a² - b²) = (a + b)(a - b)

→ π * h * (R + r)(R - r) = 396

putting all values , and value of Eqn.(1) also in LHS,

→ (22/7) * 14 * (R + r) * 2 = 396

→ 88(R + r) = 396

dividing both sides by 88,

→ (R + r) = 4.5 cm. (Ans.)

Hence, sum of outer and inner radii (in cm) is 4.5 .

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