An ice cream is in the form of a cone surmounted by a hemisphere. If the base radius of the cone is 3.5 cm and height of the ice cream is 10 cm, then find the volume of the ice cream (in cm3).
\(\left(\pi=\frac{22}{7}\right)\)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 173.25
The volume of the ice cream is the volume of the cone plus the volume of the hemisphere. The hemisphere sits on the cone’s base, so its radius is the cone’s radius, 3.5 cm, and the height of 10 cm is the cone’s height plus that radius.
Height of the cone \(h=10-3.5=6.5\,\mathrm{cm}\)
Volume of the cone \(\displaystyle =\frac{1}{3}\pi r^2h=\frac{1}{3}\times\frac{22}{7}\times3.5\times3.5\times6.5=83.42\,\mathrm{cm^3}\) (to two decimals)
Volume of the hemisphere \(\displaystyle =\frac{2}{3}\pi r^3=\frac{2}{3}\times\frac{22}{7}\times3.5\times3.5\times3.5=89.83\,\mathrm{cm^3}\) (to two decimals)
Volume of the ice cream \(=83.42+89.83=173.25\,\mathrm{cm^3}\)
Shortcut: Both parts share the factor \(\frac{1}{3}\pi r^2\), so the total is \(\frac{1}{3}\pi r^2(h+2r)\).
\(\displaystyle \frac{1}{3}\times\frac{22}{7}\times12.25\times(6.5+7)=\frac{1}{3}\times38.5\times13.5=173.25\)