3 years ago

What is the pythagorean theorem? x?

Mathematics

1 answer:

wariber [46]3 years ago

6 0

Answer:

A^2+b^2=c^2

Step-by-step explanation:

Pretty much the two shortest sides of a right triangle squared is equal to the length of the longer side (hypotenuse) squared

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olganol [36]

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3 years ago

Find the surface area of a sphere that has a volume of 288 cu. in.

LenKa [72]

The formula of a volume of a sphere:

$V=\dfrac{4}{3}\pi R^3$

R - radius

We have the volume = 288 in³. Substitute:

$\dfrac{4}{3}\pi R^3=288\qquad\text{multiply both sides by 3}\\\\4\pi R^3=864\qquad\text{divide both sides by}\ 4\pi\\\\R^3=\dfrac{216}{\pi}\to R=\sqrt[3]{\dfrac{216}{\pi}}\\\\R=\dfrac{\sqrt[3]{216}}{\sqrt[3]{\pi}}\\\\R=\dfrac{6}{\sqrt[3]{\pi}}\ in$

The formula of a surface area of a sphere:

$S.A.=4\pi R^2$

Substitute:

$S.A.=4\pi\left(\dfrac{6}{\sqrt[3]{\pi}}\right)^2=4\pi\cdot\dfrac{6^2}{\sqrt[3]{\pi^2}}=\dfrac{4\pi\cdot36}{\sqrt[3]{\pi^2}}=\dfrac{144\pi}{\sqrt[3]{\pi^2}}\\\\S.A.=\dfrac{144\pi}{\sqrt[3]{\pi^2}}\cdot\dfrac{\sqrt[3]{\pi}}{\sqrt[3]{\pi}}=\dfrac{144\pi\sqrt[3]{\pi}}{\sqrt[3]{\pi^3}}=\dfrac{144\pi\sqrt[3]{\pi}}{\pi}=\boxed{144\sqrt[3]{\pi}\ in^2}$