Question

A solid is in the form of a cylinder with hemispherical ends of the same radii. The total height of the solid is 20 cm and the diameter of the cylinder is 14 cm. Find the surface area of the solid.

Answer 1

- The solid consists of a cylindrical part and two hemispherical ends. The total height of the solid is the sum of the height of the cylinder and the height of the two hemispheres.

- Let the radius of the cylinder be \(r = \frac{14}{2} = 7 \, \text{cm}\).

- The height of the cylinder is:

\(h = 20 - 2r = 20 - 2(7) = 6 \, \text{cm}\).

- Surface area of the solid is the sum of the curved surface area of the cylinder and the surface area of the two hemispheres:

\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh + 2\pi r^2 \]

Substituting values:

\[ \text{Surface Area} = 2\pi (7)^2 + 2\pi (7)(6) + 2\pi (7)^2 = 2\pi (49) + 2\pi (42) + 2\pi (49) \]

\[ \text{Surface Area} = 2\pi (49 + 42 + 49) = 2\pi (140) = 280\pi \, \text{cm}^2 \]

Therefore, the surface area is:

\[ \text{Surface Area} = 280\pi \, \text{cm}^2 \approx 880 \, \text{cm}^2 \]