Question

 Amy measures the slant height of a cone-shaped cup and finds that it is 12 cm. The height is 10 cm. Determine the volume of water in the cup if Amy fills it to the top.

Answer 1

Explanations & Calculations

• If the radius of the base of the cone (the circle) is r, then considering a cross section of the cone through a diameter of the base circle, you can sense of a usage of Pythagoras theorem to find the radius (r) of the base.
• Therefore,

$\qquad\qquad \begin{aligned} \small r^2+(10cm)^2 &= \small (12cm)^2\\ \small r&= \small \sqrt{12^2-10^2}\\ &= \small \bold{2\sqrt{11} cm} \end{aligned}$

• And the volume of a cone is given is

$\qquad\qquad \begin{aligned} \small V &= \small \frac{1}{3}\pi r^2h\\ \small \end{aligned}$

• Therefore knowing both r & h, the volume is

$\qquad\qquad \begin{aligned} \small V&= \small \frac{1}{3}\times\pi \times(2\sqrt{11}cm)^2\times10cm\\ \small &= \small \bold{460.767cm^3} \end{aligned}$