Respuesta :

Answer:

454.5 cm³

Step-by-step explanation:

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

V= [tex]\frac{4}{3}[/tex]πr³ ← r is the radius

Thus the volume (V) of a hemisphere is

V = [tex]\frac{1}{2}[/tex] × [tex]\frac{4}{3}[/tex]πr³ = [tex]\frac{2}{3}[/tex]πr³

[tex]V_{wood}[/tex] = [tex]V_{external}[/tex] - [tex]V_{internal}[/tex]

                               = [tex]\frac{2}{3}[/tex]π × 9³ - [tex]\frac{2}{3}[/tex]π × 8³

                              = [tex]\frac{2}{3}[/tex]π (9³ - 8³)

                             = [tex]\frac{2}{3}[/tex]π (729 - 512 )

                            = [tex]\frac{2}{3}[/tex]π × 217 ≈ 454.5 cm³

gmany

Answer:

[tex]\large\boxed{V=\dfrac{434\pi}{3}\ cm^3}[/tex]

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:

[tex]V_s=\dfrac{4}{3}\pi R^3[/tex]

R - radius

Therefore the formula of a volume of a hemisphere:

[tex]V_{hs}=\dfrac{1}{2}\cdot\dfrac{4}{3}\pi R^3=\dfrac{2}{3}\pi R^3[/tex]

The volume of the larger hemisphere:

[tex]V_l=\dfrac{2}{3}\pi(9^3)=\dfrac{2}{3}\pi(729)=(2)(\pi)(243)=486\pi\ cm^3[/tex]

The volume of the smaller hemisphere:

[tex]V_s=\dfrac{2}{3}\pi(8^3)=\dfrac{2}{3}\pi(512)=\dfrac{1024\pi}{3}\ cm^3[/tex]

The volume of wood:

[tex]V=V_l-V_s[/tex]

Substitute:

[tex]V=486\pi-\dfac{1024\pi}{3}=\dfrac{1458\pi}{3}-\dfrac{1024\pi}{3}=\dfrac{434\pi}{3}\ cm^3[/tex]