2023-03-07

The volume of a cone is 141.3 cubic inches. The height of the cone is 15 inches What is the radius of the cone, rounded to the nearest inch?

pritajena90k

The formula for the Volume of a cone is:
$V=\pi {r}^{2}\frac{h}{3}$
Where:
$V$ is the Volume of the cone: $141.3{\text{in}}^{3}$ for this problem.
$r$ is the radius of the cone: what we are solving for in this problem.
$h$ is the height of the cone: $15\text{in}$ for this problem.
Substituting and solving for $r$ gives:
$141.3{\text{in}}^{3}=\pi ×{r}^{2}×\frac{15\text{in}}{3}$
$141.3{\text{in}}^{3}=\pi ×{r}^{2}×5\text{in}$
$\frac{141.3{\text{in}}^{3}}{5\text{in}}=\frac{\pi ×{r}^{2}×5\text{in}}{5\text{in}}$
$\frac{141.3{\text{in}}^{\overline{)3}2}}{5\overline{)\text{in}}}=\frac{\pi ×{r}^{2}×\overline{)5\text{in}}}{\overline{)5\text{in}}}$
$\frac{141.3{\text{in}}^{2}}{5}=\pi {r}^{2}$
$28.26{\text{in}}^{2}=\pi {r}^{2}$
$\frac{28.26{\text{in}}^{2}}{\pi }=\frac{\pi {r}^{2}}{\pi }$
$\frac{28.26{\text{in}}^{2}}{\pi }=\frac{\overline{)\pi }{r}^{2}}{\overline{)\pi }}$
$\frac{28.26{\text{in}}^{2}}{\pi }={r}^{2}$
We can use 3.1416 to estimate $\pi$ giving:
$\frac{28.26{\text{in}}^{2}}{3.1416}={r}^{2}$
$9{\text{in}}^{2}={r}^{2}$ rounded to the nearest inch.
To calculate the radius of the cone while keeping the equation balanced, take the square root of each side of the equation:
$\sqrt{9{\text{in}}^{2}}=\sqrt{{r}^{2}}$
$3\text{in}=r$
$r=3\text{in}$
The cone's radius is 3 inches, rounded to the nearest inch.

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