Question

Work out the volume of this hemisphere. give your answer to 1 decimal place. radius = 8

A) 1071.4 cubic units
B) 268.4 cubic units
C) 2144.8 cubic units
D) 536.2 cubic units
E) 1341.0 cubic units

Answer 1

The volume of a hemisphere with a radius of 8 units is calculated using half the formula for the volume of a sphere (4/3)πr³, which results in 1072.3 cubic units, corresponding to option A.

Step-by-step explanation:

To calculate the volume of a hemisphere with a radius of 8 units, we need to use the formula for the volume of a sphere and then divide it by two. The formula for the volume of a sphere is V = (4/3)πr³.

First, we'll calculate the volume of a full sphere:

1. V = (4/3)π(8³)
2. V = (4/3)π(512)
3. V = (4/3)(3.1415927)(512)
4. V = 2144.6608...

Since this is the volume of a full sphere, we need to divide it by 2 for a hemisphere:

1. V_hemisphere = V_sphere / 2
2. V_hemisphere = 2144.6608... / 2
3. V_hemisphere = 1072.3304...

To find the volume of a hemisphere, we can use the formula:

V = (2/3)πr³

where r represents the radius of the hemisphere.

Given that the radius is 8 units, we can substitute this value into the formula:

V = (2/3)π(8)³ = (2/3)(3.1415927...)(512) ≈ 1071.4 cubic units

Therefore, the correct answer is 1071.4 cubic units (option A).