Question

A solid is in the shape of a cylinder with a cone attached at one end and a
hemisphere attached to the other end as shown in the figure. All of them
are of the same radius 7 cm. If the total length of the solid is 61 cm and
height of the cylinder is 30 cm, calculate the cost of painting the outer
surface of the solid at the rate of Rs. 10 per 100 cm
​

Answer 1

The total cost of painting the outer surface of the solid at the rate of Rs. 10 per 100 $cm^2$  is Rs. 1095.

To calculate the cost of painting the outer surface of the solid, we first need to find the total surface area of the solid.

The surface area of the cylinder is 2π$r(r + h)$ = 2π(7)(37) = $506π cm^2$

The surface area of the cone is πr(√($r^2 + h^2))$= π(7)(√($7^2 + 30^2$)) = $491 \pi cm^2$

The surface area of the hemisphere is 2πr^2 =$2\pi(7^2) = 98\pi cm^2$

The total surface area of the solid is the sum of the surface area of the cylinder, cone, and hemisphere: 506π + 491π + 98π = 1095π cm^2

To calculate the cost of painting the outer surface of the solid, we need to divide the total surface area by 100 and multiply by the rate of Rs. 10 per 100 cm²

So, the cost of painting the outer surface of the solid is (1095π/100)*10 = Rs. $109.5 * 10$ = Rs. 1095

So, the total cost of painting the outer surface of the solid at the rate of Rs. 10 per $100 cm^2$ is Rs. 1095.

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