Question

It cost Rs2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per square metre, find

(i) Inner curved surface area of the vessel,

(ii) radius of the base,

(iii) total surface area

(iv) capacity of the vessel.​

Answer 1

$\huge\mathfrak\red{Answer}$

(i)

Cost of Painting = Inner CSA × Rate of Painting.

Rs 2200 = Inner CSA × 20

$\frac{2200}{20} = inner \: CSA$

Therefore, Inner CSA = 110m²

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(ii)

Let Radius be r

Height = 10m

We know that, CSA of cylinder = 110m²

$2 \: \pi \: r \: h \: = 110 {m}^{2} \\ = > 2 \times \frac{22}{7} \times r \times 10m = 110 {m}^{2} \\ = > r = \frac{110 \times 7}{2 \times 22 \times 10} \\ = > r = \frac{7}{4}$

Therefore, r = 1.75m

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(iii)

Total Surface Area =

$2\pi \: r(h + r) \\ = 2 \times \frac{22}{7} \times 1.75m(10m \: + 1.75m) \\ = 2 \times 22 \times 0.25m \times 11.75m \\ 129.25 {m}^{2}$

Therefore, TSA = 129.25m²

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(iv)

Capacity of the vessel =

$\pi {r}^{2} h \\ = \frac{22}{7} \times 1.75m \times 1.75m \times 10m \\ = {22} \times 0.25m \times 1.75m \times 10m \\ = 96.25m^{3}$

Therefore, Capacity of vessel is 96.25m³

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