The image below shows the rectangle inscribed in the circle. Dividing the rectangle into two triangles allows us to find the diameter of the circle, which is equal to the length of the line we drew. Using a²+b²= c² we get 6² + 8² = c². c² = 100, so c = 10. The area of a circle is  . Radius is half of the diameter of the circle (which we know is 10), so r = 5.

The following diagram will help to explain the solution:

We are searching for the surface area of the shaded region.  We can multiply this by the depth (1.5 feet) to find the total volume of this area.

The radius of the outer circle is 44 feet.  Therefore its area is 44²π = 1936π.  The area of the inner circle is 40²π = 1600π.  Therefore the area of the shaded area is 1936π – 1600π = 336π.  The volume is 1.5 times this, or 504π.

The area of a circle can be solved using the equation  

The area of a circle with radius 4 is while the area of a circle with radius 2 is .

In order to find the area of a circle with a known circumference, first solve for the radius of the circle.

We know the circumference of a circle is equivalent to , where .

The radius of a circle is equal to half the diameter.

Therefore:

The area of a circle is given by the equation . Use the radius to solve for the area.

The area of a circle with circumference  is  square feet.

A perimeter of a square is equal to the sum of the four equal sides:

Therefore, the length of one side of this square is 12:

We know the largest circle that can fit entirely inside the square will have a maximum diameter of 12 (the length of one side of the square).

To find the area of this circle, we must find the radius by dividing the diameter by 2:

The radius of the circle is 6. Using the formula for area, we find:

The area of the largest circle that will fit inside a square with a perimeter of 48 inches is  square inches.

This question asks you to apply the concept of area in finding both the area of a circle and square. Since the cirlce is inscribed in the square, we know that its diameter (two times the radius) is the same length as one side of the square. Since we are given the radius, , we can find the area of both the circle and square.

Square:

This gives us the area for the entire square.

The bottom half of the square has area .

Now that we have this value, we must find the area that the circle occupies. The area of a circle is given by .

So the area of this circle will be .

The bottom half of the circle has half that area:

Now that we have both our values, we can subtract the bottom half of the circle from the bottom half of the square to give us the shaded region:

We need to find the area of both the square and the circle and then subtract the two.  Inscribed means draw within a figure so as to touch in as many places as possible.  So the circle is drawn inside the square.  The opposite is circumscribed, meaning drawn outside.

A_square = s² = 36 cm² so the side is 6 cm

6 cm is also the diameter of the circle and thus the radius is 3 cm

A circle = πr² = 3.14 * 3² = 28.28 cm²

The resulting difference is 7.74 cm²

We can find the area of the shaded region by subtracting the area of the semicircles, which is much easier to find. Two semi-circles are equivalent to one full circle. Thus we can just use the area formula, where r = 6:

π(6²) → 36π

Now we must subtract the area of the semi-circles from the total area of the square. Since we know that the radius also covers half of a side, 6(2) = 12 is the full length of a side of the square. Squaring this, 12² = 144. Subtracting the area of the circles, we get our final terms,

= 144 – 36π

First find the area of both squares using the formula .

For square A, s = 5.

For square B, s = 25.

The question is asking for the ratio of these two areas, which will tell us how many times bigger square B is. Divide the area of square B by the area of square A to find the answer.