Respuesta :

Answer:

V = 756π cm³

Step-by-step explanation:

The solid shape consists of a cone and a semi sphere

To calculate the volume of the semi sphere we require to find its radius r

Given

volume of cone = 270π , then

[tex]\frac{1}{3} [/tex] πr²h = 270π ( multiply both sides by 3 to clear the fraction )

πr²h = 810π ( divide both sides by π )

r²h = 810

from diagram h = 10

10r² = 810 ( divide both sides by 10 )

r² = 81 ( take square root of both sides )

r = [tex]\sqrt{81} [/tex] = 9

Volume of semi sphere = [tex]\frac{2}{3} [/tex] πr³

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

                                       = [tex]\frac{2}{3} [/tex] π × 729

                                      = 2π × 243

                                      = 486π

The volume (V) of the solid shape

V = 270π + 486π = 756π cm³

profereyes12122

Answer:

[tex]v=756\pi cm^{3} [/tex]

Step-by-step explanation:

The radio of the cone:

[tex]270=\frac{1}{3} r^{2} (10)[/tex]

[tex]r^{2} =\frac{3(270)}{10} =810/10[/tex]

[tex]r^{2} =81[/tex]

[tex]r=\sqrt{81} =9[/tex]

The half sphere (has the same radio):

[tex]v=\frac{2}{3} \pi (9)^{3} =486\pi [/tex]

The volume of the solid shape:

[tex]v=270\pi +486\pi =756\pi cm^{3} [/tex]

Hope this helps

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