Question

A hemispherical wooden bowl has an internal radius of 8cm and an external radius of 9cm

Answer 1

Answer:

$\large\boxed{V=\dfrac{434\pi}{3}\ cm^3}$

Step-by-step explanation:

We have a hemisphere with a radius 9 cm with a hemisphere cut out with radius 8cm.

Calculate a volume of a larger hemisphere and subtract from it a volume of smaller hemisphere.

The formula of a volume of a sphere:

$V_s=\dfrac{4}{3}\pi R^3$

R - radius

Therefore the formula of a volume of a hemisphere:

$V_{hs}=\dfrac{1}{2}\cdot\dfrac{4}{3}\pi R^3=\dfrac{2}{3}\pi R^3$

The volume of the larger hemisphere:

$V_l=\dfrac{2}{3}\pi(9^3)=\dfrac{2}{3}\pi(729)=(2)(\pi)(243)=486\pi\ cm^3$

The volume of the smaller hemisphere:

$V_s=\dfrac{2}{3}\pi(8^3)=\dfrac{2}{3}\pi(512)=\dfrac{1024\pi}{3}\ cm^3$

The volume of wood:

$V=V_l-V_s$

Substitute:

$V=486\pi-\dfac{1024\pi}{3}=\dfrac{1458\pi}{3}-\dfrac{1024\pi}{3}=\dfrac{434\pi}{3}\ cm^3$

Answer 2

Answer:

454.5 cm³

Step-by-step explanation:

The volume (V) of a sphere is calculated using formula

V= $\frac{4}{3}$πr³ ← r is the radius

Thus the volume (V) of a hemisphere is

V = $\frac{1}{2}$ × $\frac{4}{3}$πr³ = $\frac{2}{3}$πr³

$V_{wood}$ = $V_{external}$ - $V_{internal}$

                               = $\frac{2}{3}$π × 9³ - $\frac{2}{3}$π × 8³

                              = $\frac{2}{3}$π (9³ - 8³)

                             = $\frac{2}{3}$π (729 - 512 )

                            = $\frac{2}{3}$π × 217 ≈ 454.5 cm³