CALC 1: Spud's mom is going to make him a round birthday cake, and has asked for your help. Spud is a bit weird, and has already

Response:

BD equals 19

Detailed breakdown:

An acute angle measures under 90°. An angle bisector is a ray that divides an angle into two equal neighboring angles. For example, if you have an angle of 270°, which exceeds a semicircle, it divides into two angles of 135° each. In this instance, the resulting angles are not acute; rather, they are obtuse.

A right triangle will have 2.2 km as its hypotenuse, with an angle of 0.5 degrees and an unknown height (see attachment).

Remember to apply the trigonometric ratios: sine, cosine, and tangent for right triangles.
Sin<span>θ = opposite side/hypotenuse
</span>Cos<span>θ = adjacent side/hypotenuse
</span>tan<span>θ = opposite side / adjacent side
</span>In this scenario, θ signifies the angle (not the right angle), which is given as 0.5°.

For this problem, we use sine as we have the side opposite the angle (the unknown height h) and the hypotenuse, with sine relating these two sides.

Let h represent the unknown opposite side, the height.
sin(0.5°) = h / (2.2km)
h = (2.2km)sin(0.5<span>°)
h = 0.019 km

I hope this has clarified your question! If you need clarification on any steps, please ask below.</span>

Step

Calculate the volume of a cylinder

We understand that

the volume of a cylinder can be expressed as

In this scenario

Insert the values

Step

Calculate the volume of a cone

We are aware that

the volume of a cone equals

In this example

Use the Pythagorean Theorem to determine the height h

Step

Calculate the empty volume inside the cylinder

Thus

the final result is

the empty volume inside the cylinder is

<span><span>Center coordinates: (x0, y0, z0)</span></span> and radius r.

<span>The equation of the sphere is:</span>
<span>(x - x0)^2 + (y - y0)^2 + (z - z0)^2 = r^2</span>