<img src="https://tex.z-dn.net/?f=%20%7B3%7D%5E%7Bb%7D%20%20%3D%2017" id="TexFormula1" title=" {3}^{b} = 17" alt=" {3}^{b} = 1

Assoli18 [71]

3 years ago

7" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

gtnhenbr [62]3 years ago

3 0

Answer:

12^3

Step-by-step explanation:

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Work out the volume of the shape

pashok25 [27]

Answer:

$\large\boxed{V=\dfrac{1,421\pi}{3}\ cm^3}$

Step-by-step explanation:

We have the cone and the half-sphere.

The formula of a volume of a cone:

$V_c=\dfrac{1}{3}\pi r^2H$

r - radius

H - height

We have r = 7cm and H = (22-7)cm=15cm. Substitute:

$V_c=\dfrac{1}{3}\pi(7^2)(15)=\dfrac{1}{3}\pi(49)(15)=\dfrac{735\pi}{3}\ cm^3$

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 half-sphere:

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

We have R = 7cm. Substitute:

$V_{hs}=\dfrac{2}{3}\pi(7^3)=\dfrac{2}{3}\pi(343)=\dfrac{686\pi}{3}\ cm^3$

The volume of the given shape:

$V=V_c+V_{hs}$

Substitute:

$V=\dfrac{735\pi}{3}+\dfrac{686\pi}{3}=\dfrac{1,421\pi}{3}\ cm^3$

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Well the line is called a ray because because the left of the endpoint is a dot and it doesn't go anywhere. So your answer is a ray.

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