Question

the difference between the outer csa and the inner csa of a cylindrical pipe is 352 sq cm .if its h is 28 cm and the volume iof material is 704 cb cm ;find its external csa​

Answer 1

Step-by-step explanation:

Let:

Outer radius = R

Inner radius = r

Outer csa - inner csa = 352 (Given)

$2\pi \: R \: h - 2\pi \: r \: h = 352 \\ 2\pi \: h(R \: - r) = 352 \\ (R \: - r) = \frac{352}{2 \times \pi \times 28} \\ = \frac{352 \times 7}{2 \times 22 \times 28} = 2 \\ (R \: - r) =2 \: \: ...(i) \\ outer \: vol \: - internal \: vol \: = 704 \\ \pi {R}^{2} h - \pi \: {r}^{2} h = 704 \\ \pi \: h( {}R^{2} - {r}^{2} ) = 704 \\ \pi \: h(R - r)(R + r) = 704 \\ \pi \: 28 \times 2(R + r) = 704 \\ (R + r) = \frac{704 \times 7}{22 \times 28 \times 2} = 4 \\ (R + r) = 4 \: \: ....(ii) \\ adding \: equations \: (i) \: and \: (ii) \\ 2R = 6 \\ R = 3 \: cm \\ external \: csa \: = 2\pi \: R \: h \\ = 2 \times \frac{22}{7} \times 3 \times 28 \\ = 528 \: {cm}^{2}$