Question

A juice glass is cylindrical in shape with a hemispherical raised-up portion at the bottom. The inner diameter of the glass is 10 cm and its height is 14 cm. Find the capacity of the glass. (use π = 3.14)

Answer 1

- The inner radius of the glass is \( r = \frac{10}{2} = 5 \, \text{cm} \).

- The height of the cylindrical part is:

\( h = 14 - 5 = 9 \, \text{cm} \).

- The volume of the cylindrical part is given by:

\[ V_{\text{cylinder}} = \pi r^2 h = 3.14 \times (5)^2 \times 9 = 3.14 \times 25 \times 9 = 706.5 \, \text{cm}^3 \]

- The volume of the hemispherical portion is:

\[ V_{\text{hemisphere}} = \frac{2}{3} \pi r^3 = \frac{2}{3} \times 3.14 \times (5)^3 = \frac{2}{3} \times 3.14 \times 125 = 261.67 \, \text{cm}^3 \]

- Therefore, the total volume (capacity) of the glass is:

\[ \text{Total Volume} = 706.5 + 261.67 = 968.17 \, \text{cm}^3 \]