# Find the volume of a right circular cone that has a height of 18.9 inches and a base with a circumference of 15 in.

Find the volume of a right circular cone that has a height of 18.9 inches and a base with a circumference of 15 in.

1. $$\bf\green{QuestioN:-}$$

Find the volume of a right circular cone that has a height of 18.9 inches and a base with a circumference of 15 inches.

$$\bf\blue{AnsweR:-}$$

As we know,

Volume of right circular cone = ⅓ (Base area × Height)

Where as,

Base Area = π r^2

Hence, Volume = ⅓ π r^2 h

Here,

Height = 18.9 inches

Circumference of the base = 15 inches

We know,

Circumference = 2πr or πd

$$\implies\bf{15 = \dfrac{22}{7}\times{r}}$$

$$\implies\bf{r = \dfrac{15\times7}{22}}$$

$$\implies\bf{r= 4.7\:inches}$$

Now we can see the volume of this right circular cone,

Formula applied here = ⅓ π r^2 h

Radius = 4.7 inches

Height = 18.9 inches

Volume = ⅓ π r^2 h

$$\implies\bf{\dfrac{1}{3}\times\dfrac{22}{7}\times4.7^{2} \times18.9}$$

$$\implies\bf{\dfrac{22}{21}\times22.09 \times18.9}$$

$$\implies\bf{437.382\:cubic\;units}$$

The required answer for your question is,

$$\Large\pink\pmb{\bigstar437.382\:cubic\:units!!}$$

All Done!! ☺