A sphere and a cone have the same volume. each figure has a radius of 3 inches.

1 answer:

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The volume of a sphere - $\frac{4}{3} \pi r^3$
The volume of a cone - $\frac{1}{3} \pi r^2 h$
r - radius, h - height

The sphere and the cone have the same volume and the radius is 3 inches.
$\frac{4}{3} \pi \times 3^3=\frac{1}{3} \pi \times 3^2 \times h \ \ \ |\div \pi \\
\frac{4}{3} \times 27=\frac{1}{3} \times 9 \times h \\
36=3h \ \ \ |\div 3 \\
h=12$

The height of the cone is 12 inches.

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Angle sum theory find Y

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<h3>Answer:</h3>

<h3>Step-by-step explanation:</h3>

The angle sum theory says that the sum of all the interior angles in a triangle is 180 degrees.

Finding X

To solve for y, we must first find x. This way we know 2 of the interior angles. Luckily, angle x is a part of a linear pair.

Linear Pairs are 2 adjacent angles that create a straight line together. This means that the sum to 180 degrees.

Angle x and the angle with a measurement of 115 form a linear pair. Thus, we can create an equation to find x.

115 + x = 180

By subtracting 115 from both sides we know that x = 65.

Solving for Y

Now that we know x, we can find y. We know that one of the interior angles is 65 and that the other is 90 degrees. The square marking the bottom angles in the middle show that they are right angles.