Exercise 37 Page 638

A hemisphere is the name of a solid that is half of a sphere.

Therefore, the volume of a hemisphere with radius

r

is half the volume of a sphere with radius

r .

\underline{Volume of a Hemisphere} V = \frac{1}{2} (\frac{4}{3} π r^{3}) \Leftrightarrow V = \frac{2}{3} π r^{3}

To use this formula we first need to calculate the radius. To do so, we will consider the given hemisphere.

In the diagram we can see that the radius is

1.4

meters. We can substitute this value for

r

in the formula for the volume of a hemisphere and evaluate.

V = \frac{2}{3} π r^{3}

$r = 1.4$

V = \frac{2}{3} π (1.4)^{3}

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Evaluate right-hand side

Calculate power

V = \frac{2}{3} π (2.744)

Commutative Property of Multiplication

V = \frac{2}{3} (2.744) π

$\frac{a}{c} \cdot b = \frac{a \cdot b}{c}$

V = \frac{2 ( 2 . 7 4 4 )}{3} π

V = \frac{5 . 4 8 8}{3} π

Use a calculator

V = 5.747020 \dots

Round to $1$ decimal place(s)

V \approx 5.7

The volume of the hemisphere, to the nearest tenth, is

5.7

cubic meters.