Question

What is the volume of a hemisphere with a diameter of 47.5 m, rounded to the nearest tenth of a cubic meter?

Answer 1

Explanation:

What is the volume of a hemisphere with a diameter of 37.6 m, rounded to the of a cubic meter?

\text{Volume of a Sphere:}

Volume of a Sphere:

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

V=

3

4

​

πr

3

\text{radius} = \frac{\text{diameter}}{2} = \frac{37.6}{2}=18.8

radius=

2

diameter

​

=

2

37.6

​

=18.8

meters

\text{Plug in:}

Plug in:

\frac{4}{3}\pi (18.8)^3

3

4

​

π(18.8)

3

27833.1369876

27833.1369876

Use calculator

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

Volume of Hemisphere HALF of Volume of Sphere:

\frac{27833.1369876}{2}

2

27833.1369876

​

Divide volume by 2

13916.5684938

13916.5684938

\approx 13916.6\text{ m}^3

≈13916.6 m

3

Round to the nearest tenth

Answer 2

28043.3
`m^(3)`

Explanation:

Formula for volume of a hemisphere can be termed as:

`V = (2)/(3) \pi r^(3)`

where
`r` is the radius of hemisphere

Please refer to the figure attached for the sample figure of a hemisphere.

We are given here, diameter of hemisphere = 47.5 m

Relation between diameter and radius is given as :

`r = (d)/(2)`

where,
`r` is the radius and

`d` is the diameter.

So,
`r = (47.5)/(2)\ m`

Volume is:

`V = (2)/(3) \pi ((47.5)/(2))^3\\\Rightarrow (2)/(3) * 3.14 * ((47.5)/(2))^3\\\Rightarrow 28043.3\ m^3`

Hence, volume of given hemisphere is 28043.3
`m^(3)`.