Question

Find the following measures for this figure.
Lateral Area = 55 square units 5√(47) square units 5√(146) square units
Volume = 275 cubic units 91 2/3 cubic units 36 2/3 cubic units

Answer 1

1. We can find lateral area of a cone by $\text{Lateral area}=\pi*r*l$, where r equals radius of cone and l equals slant height of cone.

We can find slant height of our cone using Pythagorean theorem.

$l=\sqrt{11^{2}+5^{2}}$

$l=\sqrt{121+25}$

$l=\sqrt{146}$

Let us substitute our slant height in lateral area formula.

$\text{Lateral area}=\pi*5\sqrt{146}$

Therefore, our lateral area will be $\pi*5\sqrt{146}$ square units.

2. $\text{Volume of cone}=\frac{1}{3} \cdot\pi\cdot r^{2}\cdot h$

Upon substituting our given values in volume formula we will get,

$\text{Volume of cone}=\frac{1}{3} \cdot\pi\cdot 5^{2}\cdot 11$

$\text{Volume of cone}=\frac{1}{3} \cdot\pi \cdot 25\cdot 11$

$\text{Volume of cone}=\frac{275}{3} \cdot\pi$

$\text{Volume of cone}=91\frac{2}{3} \cdot\pi$

Therefore, volume of our cone will be $91\frac{2}{3} \cdot\pi$ cubic units.