What is the diameter of a hemisphere with a volume of 8280ft^(3), to the nearest tenth of a foot? Answer: ft

Volume Formula Derivation: To find the diameter of the hemisphere, we first need to know the formula for the volume of a hemisphere, which is (2/3)πr^3, where r is the radius of the hemisphere. We are given the volume, so we need to solve for r and then double it to find the diameter.Volume Equation Setup: We set up the equation (2/3)πr^3 = 8280 ft^3 and solve for r. First, we divide both sides by (2/3)π to isolate r^3. r^3 = 8280 ft^3 / ((2/3)π)Calculate Volume: Now we calculate the right side of the equation using the value of π as approximately 3.14159. r^3 = 8280 ft^3 / ((2/3) * 3.14159) r^3 ≈ 8280 ft^3 / 2.09439 r^3 ≈ 3953.76 ft^3Calculate Radius: Next, we take the cube root of both sides to solve for r. r ≈ (3953.76 ft^3)^(1/3) r ≈ 15.8 ftCalculate Diameter: Since the diameter is twice the radius, we multiply r by 2 to find the diameter. Diameter = 2 * r Diameter ≈ 2 * 15.8 ft Diameter ≈ 31.6 ft

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the diameter of a hemisphere with a volume of
8280ft^(3), to the nearest tenth of a foot?
Answer:
ft

What is the diameter of a hemisphere with a volume of $8280 \mathrm{ft}^{3}$ , to the nearest tenth of a foot? $\newline$ Answer: $\mathrm{ft}$

View step-by-step help

Home

Math Problems

Grade 7

Convert between customary and metric systems

Full solution

Q. What is the diameter of a hemisphere with a volume of

8280 \mathrm{ft}^{3}

, to the nearest tenth of a foot?

\newline

Answer:

\mathrm{ft}

Volume Formula Derivation: To find the diameter of the hemisphere, we first need to know the formula for the volume of a hemisphere, which is $(\frac{2}{3})\pi r^3$ , where $r$ is the radius of the hemisphere. We are given the volume, so we need to solve for $r$ and then double it to find the diameter.
Volume Equation Setup: We set up the equation $(\frac{2}{3})\pi r^3 = 8280 \text{ ft}^3$ and solve for $r$ . First, we divide both sides by $(\frac{2}{3})\pi$ to isolate $r^3$ . $r^3 = \frac{8280 \text{ ft}^3}{((\frac{2}{3})\pi)}$
Calculate Volume: Now we calculate the right side of the equation using the value of $\pi$ as approximately $3.14159$ . $r^3 = \frac{8280 \text{ ft}^3}{\left(\frac{2}{3}\right) \cdot 3.14159}$ $r^3 \approx \frac{8280 \text{ ft}^3}{2.09439}$ $r^3 \approx 3953.76 \text{ ft}^3$
Calculate Radius: Next, we take the cube root of both sides to solve for $r$ . $r \approx (3953.76 \, \text{ft}^3)^{1/3}$ $r \approx 15.8 \, \text{ft}$
Calculate Diameter: Since the diameter is twice the radius, we multiply $r$ by $2$ to find the diameter. $\text{Diameter} = 2 \times r$ $\text{Diameter} \approx 2 \times 15.8 \, \text{ft}$ $\text{Diameter} \approx 31.6 \, \text{ft}$