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
Answers
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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