Question

What is the diameter of a hemisphere with a volume of 257 m^3

Answer 1

Answer:

9.9

Step-by-step explanation:

\text{Volume of Hemisphere}\text{:}

Volume of Hemisphere:

\,\,257

257

\text{Volume of Sphere}\text{:}

Volume of Sphere:

\,\,514

514

Double volume of hemisphere to get volume of the entire sphere

\text{Volume of a Sphere:}

Volume of a Sphere:

V=\frac{4}{3}\pi r^3

V=

3

4

​

πr

3

514=

514=

\,\,\left(\frac{4}{3}\pi\right) r^3

(

3

4

​

π)r

3

514=

514=

\,\,(4.1887902)r^3

(4.1887902)r

3

Evaluate 4/3pi in calc

\frac{514}{4.1887902}=

4.1887902

514

​

=

\,\,\frac{(4.1887902)r^3}{4.1887902}

4.1887902

(4.1887902)r

3

​

Evaluate \frac{4}{3}\pi

3

4

​

π in calc

122.7084611=

122.7084611=

\,\,r^3

r

3

\sqrt[3]{122.7084611}=

3

 

122.7084611

​

=

\,\,\sqrt[3]{r^3}

3

 

r

3

​

Cube root both sides

4.9692575=

4.9692575=

\,\,r

r

\text{Then the diameter equals }9.938515

Then the diameter equals 9.938515

diameter is radius times 2

\text{Final Answer:}

Final Answer:

d\approx 9.9\text{ m}

d≈9.9 m

Round to nearest tenth