Question

It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10m deep. If the cost of painting is at the rate of Rs 20 per m?, find
(i) inner curved surface area of the vessel
(ii) radius of the base
(iii) capacity of the vessel (Assume π = 22/7)​

Answer 1

Answer:

$\:\boxed{\begin{aligned}& \:\sf \:Inner \: curved\:surface\:area \: of \: vessel \: = \:110 \: {m}^{2} \: \\ \\& \:\sf \: Radius \: of \: vessel \: = \: \dfrac{7}{4} \: m \\ \\& \:\sf \:Capacity\:of\:cylindrical\:vessel = \:96.25 \: {m}^{3}\end{aligned}} \qquad \:$

Step-by-step explanation:

Let assume that r and h represents the radius and height of cylindrical vessel respectively.

Given that, It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep and the cost of painting is at the rate of Rs 20 per $m^2$.

So,

$\sf \: Curved\:surface\:area \: of \: vessel \: = \: \dfrac{2200}{20} \: {m}^{2}$

$\implies\sf \:Inner \: curved\:surface\:area \: of \: vessel \: = \:110 \: {m}^{2}$

Now,

We know,

$\sf \: Inner \:curved\:surface\:area = 2\pi \: r \: h$

$\sf \: 2 \times \dfrac{22}{7} \times r \times 10 = 110$

$\sf \: r = \dfrac{7 \times 110}{2 \times 22 \times 10}$

$\implies\sf \: r = \dfrac{7}{4} \:m$

Now, Consider

$\sf \: Capacity\:of\:cylindrical\:vessel$

$\sf \: = \: \pi {r}^{2}h$

$\sf \: = \: \dfrac{22}{7} \times \dfrac{7}{4} \times \dfrac{7}{4} \times 10$

$\sf \: = \: 11 \times \dfrac{7}{4} \times 5$

$\sf \: = \: \dfrac{385}{4}$

$\sf \: = \:96.25 \: {m}^{3}$

Hence,

$\implies\sf \: Capacity \:of\:cylindrical\:vessel = \:96.25 \: {m}^{3}$

Hence,

$\:\boxed{\begin{aligned}& \:\sf \:Inner \: curved\:surface\:area \: of \: vessel \: = \:110 \: {m}^{2} \: \\ \\& \:\sf \: Radius \: of \: vessel \: = \: \dfrac{7}{4} \: m \\ \\& \:\sf \:Capacity\:of\:cylindrical\:vessel = \:96.25 \: {m}^{3}\end{aligned}} \qquad \:$

Answer 2

Answer:

• The inner curved surface area of the vessel is 110 square meters.
• The radius of the base of the vessel is 7/4 meters.
• The capacity of the vessel is 96.25 cubic meters.

Step-by-step explanation:

Let's solve this problem step by step:

(i) Inner Curved Surface Area of the Vessel:

We know that the cost of painting is Rs. 20 per square meter.

Therefore, the total cost of painting the inner curved surface of the cylindrical vessel is:

Cost of painting = Rs. 2200

Cost per square meter = Rs. 20

Therefore, the area of the inner curved surface of the vessel can be calculated as follows:

Area = Cost of painting / Cost per square meter

Area = 2200 / 20 = 110 square meters

Hence, the inner curved surface area of the vessel is 110 square meters.

(ii) Radius of the Base:

We know that the cylindrical vessel is 10m deep.

We also know that the curved surface area of a cylinder is given by the formula:

Curved surface area = 2πrh

Where r is the radius of the base, and h is the height of the cylinder.

We can rearrange the above formula to find the radius of the base:

r = Curved surface area / 2πh

Substituting the values we have:

Curved surface area = 110 square meters

Height of the cylinder (depth of the vessel) = 10 meters

π = 22/7

Therefore, the radius of the base can be calculated as follows:

r = (110 / (2 × 22/7 × 10))

r = 7/4 meters

Hence, the radius of the base of the vessel is 7/4 meters.

(iii) Capacity of the Vessel:

The formula for the volume of a cylinder is given by:

Volume = πr²h

Substituting the values we have:

Radius of the base = 7/4 meters.

Height of the cylinder (depth of the vessel) = 10 meters

π = 22/7

Therefore, the capacity of the vessel can be calculated as follows:

Volume = (22/7) × (7/4)² × 10

Volume = 96.25 cubic meters.

Hence, the capacity of the vessel is 96.25 cubic meters.