# The radius of the larger circle is twice as long as the radius of the smaller circle. The area of the donut is 75 pi . Find the radius of the smaller (inner) circle.?

The smaller radius is 5

Let r = the radius of the inner circle.

From the reference we obtain the equation for the area of an annulus :

Substitute 2r for R:

Simplify:

Substitute in the given area:

By signing up, you agree to our Terms of Service and Privacy Policy

Let ( R ) be the radius of the larger circle and ( r ) be the radius of the smaller circle.

Given that the area of the donut is ( 75\pi ), we can express this as the difference between the areas of the larger circle and the smaller circle:

[ \pi R^2 - \pi r^2 = 75\pi ]

Given that the radius of the larger circle is twice as long as the radius of the smaller circle, we can express this as ( R = 2r ).

Substitute ( R = 2r ) into the equation:

[ \pi (2r)^2 - \pi r^2 = 75\pi ]

Simplify:

[ 4\pi r^2 - \pi r^2 = 75\pi ] [ 3\pi r^2 = 75\pi ]

Divide both sides by ( 3\pi ):

[ r^2 = 25 ]

Take the square root of both sides:

[ r = 5 ]

So, the radius of the smaller (inner) circle is ( 5 ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is #4 #, its base's sides have lengths of #8 #, and its base has a corner with an angle of #(7 pi)/8 #. What is the pyramid's surface area?
- The base of a triangular pyramid is a triangle with corners at #(2 ,4 )#, #(3 ,2 )#, and #(5 ,5 )#. If the pyramid has a height of #5 #, what is the pyramid's volume?
- A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is #8 #, its base has sides of length #4 #, and its base has a corner with an angle of #(3 pi)/8 #. What is the pyramid's surface area?
- A triangle has two corners with angles of # ( pi ) / 2 # and # ( 5 pi )/ 12 #. If one side of the triangle has a length of #9 #, what is the largest possible area of the triangle?
- What is the area of an equilateral triangle with a perimeter of 6 inches?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7