What is the volume of a hemisphere with a radius of 55.8in, rounded to the nearest tenth of a cubic inch? Answer: in ^(3)

Recall Sphere Volume Formula: Recall the formula for the volume of a sphere. The volume (V) of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. Since a hemisphere is half of a sphere, we need to divide this volume by 2 to get the volume of a hemisphere.Substitute Given Radius: Substitute the given radius into the formula for the volume of a hemisphere. The radius (r) is given as 55.8 inches. So, the volume (V) of the hemisphere is V = (1/2) * (4/3)π(55.8)^3.Calculate Volume: Calculate the volume using the substituted values. V = (1/2) * (4/3)π(55.8)^3 V = (2/3)π(55.8)^3 V = (2/3)π(55.8 * 55.8 * 55.8) V ≈ (2/3)π(175032.152)Perform Multiplication and Division: Perform the multiplication and division to find the volume. V ≈ (2/3) * π * 175032.152 V ≈ 116688.10133333333 * π V ≈ 366519.4815 cubic inches (using π ≈ 3.14159)Round to Nearest Tenth: Round the result to the nearest tenth of a cubic inch. The volume of the hemisphere, rounded to the nearest tenth, is approximately 366519.5 cubic inches.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the volume of a hemisphere with a radius of
55.8in, rounded to the nearest tenth of a cubic inch?
Answer: in
^(3)

What is the volume of a hemisphere with a radius of $55.8$ $\mathrm{in}$ , rounded to the nearest tenth of a cubic inch? $\newline$ Answer: $\text{in}$ $^{3}$

View step-by-step help

Home

Math Problems

Grade 7

Convert between customary and metric systems

Full solution

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

55.8

\mathrm{in}

, rounded to the nearest tenth of a cubic inch?

\newline

Answer:

\text{in}

^{3}

Recall Sphere Volume Formula: Recall the formula for the volume of a sphere. $\newline$ The volume $V$ of a sphere is given by the formula $V = \frac{4}{3}\pi r^3$ , where $r$ is the radius of the sphere. Since a hemisphere is half of a sphere, we need to divide this volume by $2$ to get the volume of a hemisphere.
Substitute Given Radius: Substitute the given radius into the formula for the volume of a hemisphere. $\newline$ The radius $r$ is given as $55.8$ inches. So, the volume $V$ of the hemisphere is $V = \frac{1}{2} \times \frac{4}{3}\pi(55.8)^3$ .
Calculate Volume: Calculate the volume using the substituted values. $\newline$ $V = \frac{1}{2} \times \frac{4}{3}\pi(55.8)^3$ $\newline$ $V = \frac{2}{3}\pi(55.8)^3$ $\newline$ $V = \frac{2}{3}\pi(55.8 \times 55.8 \times 55.8)$ $\newline$ $V \approx \frac{2}{3}\pi(175032.152)$
Perform Multiplication and Division: Perform the multiplication and division to find the volume. $\newline$ $V \approx \frac{2}{3} \times \pi \times 175032.152$ $\newline$ $V \approx 116688.10133333333 \times \pi$ $\newline$ $V \approx 366519.4815$ cubic inches (using $\pi \approx 3.14159$ )
Round to Nearest Tenth: Round the result to the nearest tenth of a cubic inch. $\newline$ The volume of the hemisphere, rounded to the nearest tenth, is approximately $366519.5$ cubic inches.