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sukhopar [10]
3 years ago
5

Help with spheres! I don't have to do question 3

Mathematics
1 answer:
Katena32 [7]3 years ago
6 0
Question 1.

d: diameter of the sphere

r: radius of the sphere:


As we know,

r=\dfrac{d}{2}\\ \\ r=\dfrac{15}{2}~\mathrm{in}

Formula for the volume of a sphere, given its radius:

V=\dfrac{4\pi r^{3}}{3}\\ \\ \\ V=\dfrac{4\pi\cdot (\frac{15}{2})^{3}}{3}\\ \\ \\ V=\dfrac{4\pi}{3}\cdot \dfrac{15^{3}}{8}\\ \\ \\ V=\dfrac{\diagup\!\!\!\! 4 \pi}{3}\cdot \dfrac{(3\cdot 5)^{3}}{\diagup\!\!\!\! 4\cdot 2}\\ \\ \\ V=\dfrac{\pi}{3}\cdot \dfrac{3^{3}\cdot 5^{3}}{2}\\ \\ \\ V=\dfrac{\pi}{\diagup\!\!\!\! 3}\cdot \dfrac{\diagup\!\!\!\! 3\cdot 3^{2}\cdot 5^{3}}{2}\\ \\ \\ V=\pi \cdot \dfrac{9\cdot 125}{2}\\ \\ \\ \boxed{\begin{array}{c} V=\dfrac{1\,125\pi}{2}\mathrm{~in^{3}} \end{array}}


<span>Question 2.
</span>
r=6.8~\mathrm{ft}

The volume of a hemisphere is given by

V=\dfrac{2\pi r^{3}}{3}\\ \\ \\ V=\dfrac{2\pi\cdot (6.8)^{3}}{3}\\ \\ \\ V=\dfrac{2\pi\cdot 314.432}{3}\\ \\ \\ V \approx \dfrac{2*3.14*314.432}{3}\\ \\ \\ \boxed{\begin{array}{c} V \approx 658,2\mathrm{~ft^{3}} \end{array}}

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So in the end part we should arrive at a sum of products. Then you can just invert. For example, if at the end you had:

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Step-by-step explanation:

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