A piece of rectangular paper measures 8x by 12x. If a circle with a radius of 3x is cut out of the middle of the paper, what will be the area of the remaining piece of paper in terms of π?
3. A rectangular gazebo measuring 7x by 9x is built in the middle of a rectangular yard measuring 20x by 15x. How much of the yard is left over?
HELP WITH STEPS(:
Area of a circle:πr^2
Area of a rectangle: bh
Then after you've gotten that far subtract. :)
9.7 hw workshett
Sure! Let's go step by step and calculate the areas of the remaining pieces of paper and yard.
1. For the first question about the piece of rectangular paper, we need to find the area of the remaining piece after a circle with a radius of 3x is cut out of the middle.
To find the area of the paper, we can simply calculate the area of the rectangle and subtract the area of the circle. The formula for the area of a rectangle is Length x Width, and the formula for the area of a circle is π x radius^2.
Given that the dimensions of the paper are 8x by 12x, the area of the rectangle is (8x) x (12x) = 96x^2.
The radius of the circle is given as 3x, and the formula for the area of a circle is π x (3x)^2 = 9πx^2.
Therefore, the area of the remaining piece of paper is 96x^2 - 9πx^2 = (96 - 9π)x^2.
2. For the second question about the rectangular gazebo and yard, we need to find the area of the leftover yard after the gazebo is built.
Again, we can calculate the areas of the rectangle and subtract the area of the gazebo. The formula for the area of a rectangle is Length x Width.
Given that the dimensions of the yard are 20x by 15x, the area of the yard is (20x) x (15x) = 300x^2.
The dimensions of the gazebo are given as 7x by 9x, so the area of the gazebo is (7x) x (9x) = 63x^2.
Therefore, the area of the leftover yard is 300x^2 - 63x^2 = 237x^2.
That's it! You now know how to calculate the areas of the remaining pieces of paper and leftover yard.