Question

A hollow cylinder of internal radius 3 cm external radius 4 cm and height 10 cm is to be painted completely what will be the cost of painting if the rate of painting is rupees 2 per cm^2

Answer 1

SOLUTION :-

The inner radius of the hollow cylinder (r) = 3 cm

The outer radius of the hollow cylinder (R) = 4 cm

The height of the hollow cylinder (h) = 10 cm

First we have to find the TSA of the hollow cylinder.

As the painting would be done on the TSA of the hollow cylinder.

The Total Surface Area of the hollow cylinder

= = $\boxed{\boxed{ 2 \pie (R + r) (h + R - r) }}}$

= $2 \times \frac{22}{7} (R + r) (h + R - r)$

=  $\frac{44}{7} (4 + 3) (10 + 4 - 3)$

= $\frac{44}{7} \times 7 \times 11$

= $\boxed{\boxed{484 \: cm \: square}}}$

If the cost of painting 1 cm square is Rs 2,

Than,

The cost of painting the TSA of the hollow cylinder will be

= 2 × 484

= = $\boxed{\boxed{Rs \: 968 }}}$

Hence

The cost of painting the hollow cylinder is Rs 968