Question

the volume of the cone is 25.12cm cubed, and the area of the base is 12.56cm squared.what is the height

Answer 1

Height of the cone having volume as $25.12 \text { cm}^{3}$ and base area $12.56 \text { cm}^{2}$ is 6 cm.

Solution:

Given that volume of cone = $25.12 \text{ cm}^{3}$

Area of base = $12.56 \text { cm}^{2}$

Need to determine height of the cone.

Formula for volume of the cone is as follows

$\mathrm{V}_{c}=\frac{1}{3} \pi r^{2}{h} \rightarrow (1)$

Area of circular base of cone = $A_{b}=\pi r^{2}$

Replacing $\pi r^{2} \text { by } A_{b}$ in equation (1), we get

$\mathrm{V}_{\mathrm{c}}=\frac{1}{3} \mathrm{A}_{\mathrm{b}} \mathrm{h}$

$\Rightarrow \frac{3 \mathrm{V} c}{\mathrm{A}_{\mathrm{b}}}=h$

$\Rightarrow h=\frac{3 \mathrm{v} c}{\mathrm{A}_{\mathrm{b}}} \rightarrow (2)$

In our case Volume of cone $V_c= 21.12 \text{ cm}^3$ and Area of base $A_b=12.56 \text { cm}^2$

On substituting the values of volume and area in equation 2 we get

$h=\frac{3 \times 25.12}{12.56}=6 \text{ cm }$