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 object comprises a cylinder with two hemispherical ends. Its total height is the combined height of the cylindrical section and the two hemispherical caps.

- The cylinder's radius is calculated as \(r = \frac{14}{2} = 7 \, \text{cm}\).

- The height of the cylinder is determined as:

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

- The total surface area of the object is the sum of the cylinder's lateral surface area and the surface area of the two hemispheres:

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

Upon substituting the values:

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

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

Consequently, the surface area is:

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