<img src="https://tex.z-dn.net/?f=-r%2B%283r%5E%7B2%7D%2B1%29r%3D4" id="TexFormula1" title="-r+(3r^{2}+1)r=4" alt="-r+(3r^{2}+1)

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Dimas [21]

3 years ago

r=4" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

NARA [144]3 years ago

5 0

Answer:

$r = \sqrt[3]{\frac{4}{3} }$

Step-by-step explanation:

$-r + (3r^2 + 1)r = 4\\-r + 3r^3 + r = 4\\3r^3 = 4\\r^3 = \frac{4}{3} \\\\r = \sqrt[3]{\frac{4}{3} }$

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17. A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. Find

Pavlova-9 [17]

Answer:

$r = 3.74cm$

Step-by-step explanation:

Given

Hemisphere

$Radius = 7cm$

Cone

$Height = 49m$

Required

Determine the radius of the cone

First, we calculate the volume (V1) of the hemisphere.

$V_1 = \frac{2}{3}\pi r^3$

Substitute 7 for r

$V_1 = \frac{2}{3}\pi * 7^3$

$V_1 = \frac{2}{3}\pi * 343$

$V_1 = \frac{686}{3}\pi$

Volume (V2) of a cone is:

$V_2 = \frac{1}{3}\pi r^2h$

Because the lead is cast into a cone, then they have the same volume.

So, we have:

$\frac{686}{3}\pi = \frac{1}{3}\pi r^2h$

$686 = r^2h$

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$686 = r^2 * 49$

Divide both sides by 49

$r^2 = \frac{686}{49}$

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Answer:

The scale factor is 5 because the increase in each side of the shape is *5

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