Immadvapsupvkd

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

Beginner2023-03-08Added 6 answers

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:

$141.3{\text{in}}^{3}=\pi \times {r}^{2}\times \frac{15\text{in}}{3}$

$141.3{\text{in}}^{3}=\pi \times {r}^{2}\times 5\text{in}$

$\frac{141.3{\text{in}}^{3}}{{5\text{in}}}=\frac{\pi \times {r}^{2}\times 5\text{in}}{{5\text{in}}}$

$\frac{141.3{\text{in}}^{{\overline{){3}}}2}}{{5{\overline{){\text{in}}}}}}=\frac{\pi \times {r}^{2}\times {\overline{){5\text{in}}}}}{\overline{){5\text{in}}}}$

$\frac{141.3{\text{in}}^{2}}{{5}}=\pi {r}^{2}$

$28.26{\text{in}}^{2}=\pi {r}^{2}$

$\frac{28.26{\text{in}}^{2}}{{\pi}}=\frac{\pi {r}^{2}}{{\pi}}$

$\frac{28.26{\text{in}}^{2}}{{\pi}}=\frac{{\overline{){\pi}}}{r}^{2}}{\overline{){\pi}}}$

$\frac{28.26{\text{in}}^{2}}{{\pi}}={r}^{2}$

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.

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

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:

$141.3{\text{in}}^{3}=\pi \times {r}^{2}\times \frac{15\text{in}}{3}$

$141.3{\text{in}}^{3}=\pi \times {r}^{2}\times 5\text{in}$

$\frac{141.3{\text{in}}^{3}}{{5\text{in}}}=\frac{\pi \times {r}^{2}\times 5\text{in}}{{5\text{in}}}$

$\frac{141.3{\text{in}}^{{\overline{){3}}}2}}{{5{\overline{){\text{in}}}}}}=\frac{\pi \times {r}^{2}\times {\overline{){5\text{in}}}}}{\overline{){5\text{in}}}}$

$\frac{141.3{\text{in}}^{2}}{{5}}=\pi {r}^{2}$

$28.26{\text{in}}^{2}=\pi {r}^{2}$

$\frac{28.26{\text{in}}^{2}}{{\pi}}=\frac{\pi {r}^{2}}{{\pi}}$

$\frac{28.26{\text{in}}^{2}}{{\pi}}=\frac{{\overline{){\pi}}}{r}^{2}}{\overline{){\pi}}}$

$\frac{28.26{\text{in}}^{2}}{{\pi}}={r}^{2}$

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:

$\sqrt{9{\text{in}}^{2}}=\sqrt{{r}^{2}}$

$3\text{in}=r$

$r=3\text{in}$

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