Question

the difference between the outer and inner curved surface area of a right circular cylinder with 14 cm long is 88 CM square if the volume of metal used making is 176 cm cube find the outer and inner diameter of cylinder

Answer 1

Answer:The difference between the outer and inner curved surface area of a right circular cylinder with 14 cm long is 88 CM square if the volume of metal used making is 176 cm cube find the outer and inner diameter of cylinder

Step-by-step explanation:

Answer 2

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♠ Given Height (h) = 14 cm

Let the outer radius be R and inner radius be r.

Then, Outer Curved surface area (C.S.A) = 2πRh

Inner C.S.A = 2πrh

Outer Volume = πR²h

Inner Volume = πr²h

♠ Now, its given that difference between outer C.S.A and inner C.S.A is 88 cm².

$\sf{=⟩ 2 \pi R h - 2 \pi r h = 88}$

$\sf{=⟩ 2 \pi h (R - r) = 88}$

$\sf{=⟩ 2 \times \frac {22}{7} \times 14 (R - r) = 88}$

$\sf{=⟩ R - r = 88 \times \frac{1}{14} \times \frac{1}{2} \times \frac{7}{22}}$

$\sf{=⟩ R - r = 1}$....eq i

♠ Also, Volume of metal used to make the cylinder is 176 cm³

$\sf{=⟩ \pi {R}^{2} h - \pi {r}^{2} h = 176}$

$\sf{=⟩ \pi h ({R}^{2} - {r}^{2}) = 176}$

$\sf{=⟩ \frac{22}{7} \times 14 \times ({R}^{2} - {r}^{2}) = 176}$

$\sf{=⟩ ({R}^{2} - {r}^{2}) = 176 \times \frac{1}{14} \times \frac{7}{22}}$

$\sf{=⟩ ({R}^{2} - {r}^{2}) = 4 }$... eq ii

$\sf{=⟩ (R + r)(R - r) = 4}$

♠ Then, from eq i and ii,

$\sf{(R + r)(R - r) = 4}$

$\sf{=⟩ (R + r) (1) = 4}$

$\sf{=⟩ R + r = 4 \times 1}$

$\sf{=⟩ R + r = 4}$... eq iii

♠ Adding eq i and iii,

$\sf{(R - r) + (R + r) = 4 + 1}$

$\sf{=⟩ R - r + R + r = 5}$

$\sf{=⟩ 2R = 5}$

$\sf{=⟩ R = 5 \times \frac{1}{2}}$

$\sf{=⟩ R = \frac{5}{2}}$

♠ Now, substituting the value of R in eq iii,

$\sf{\frac{5}{2} + r = 4}$

$\sf{=⟩ r = 4 - \frac{5}{2}}$

$\sf{=⟩ r = \frac{3}{2}}$

♥♥♥ •°• The outer radius is 5/2 cm and inner radius is 3/2 cm. ♥♥♥

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