Question

The volume of a right circular cone is $110m^3$ and diameter is $2\sqrt{15}m$. Calculate
i) Height of the cone
ii) Slant height
iii) Curved Surface area [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 1 Mark each

Diameter
$=2\sqrt{15}m$

Radius
$=\sqrt{15}m$

$\frac{1}{3}\pi r^{2}h=110$


i) Height of the cone
$\frac{1}{3}\pi r^{2}h=110$

$\frac{1}{3}\times \frac{22}{7}\times {\left(\sqrt{15}\right)}^2\times h=110$

$h=7m$


ii) Slant Height
$l^2=h^2+r^2$

$l^2=7^2+{\left(\sqrt{15}\right)}^2$

$l=8m$

iii) Curved Surface area of the cone
$=\pi rl$

$=\frac{22}{7}\times \sqrt{15}\times 8$

$=97.3m^2$