Problem Statement
A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is $2\text{ cm}$ and the diameter of the base is $4\text{ cm}$. Determine the volume of the toy. (Take $\pi = 3.14$)
Verified Solution & Marking Scheme
Identify dimensions
Diameter of base $d = 4\text{ cm} \implies$ radius $r = 2\text{ cm}$.
Radius of hemisphere $r = 2\text{ cm}$.
Height of cone $h = 2\text{ cm}$.
Formulate combined volume
$\text{Volume of toy } V = \text{Volume of hemisphere} + \text{Volume of cone}$
$V = \frac{2}{3}\pi r^3 + \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi r^2 (2r + h)$
Substitute numerical values
$V = \frac{1}{3} \times 3.14 \times (2)^2 \times [2(2) + 2]$
$V = \frac{1}{3} \times 3.14 \times 4 \times [4 + 2] = \frac{1}{3} \times 3.14 \times 4 \times 6 = 3.14 \times 8 = 25.12\text{ cm}^3$