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5 Geometry Problems

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Please explain in full detail the steps to these problems. Do not do #25 instead explain the following:

18. What is the area of a square if the length of a diagonal is 4 sq. rt. 2?
22. The floor of a room is 120 feet by 96 feet. The ceiling is 9 feet above the floor. Everything is to be painted except the floor. (Don't worry about doors or windows). How many square yards must be painted?
NOTE: How many square feet in one square yard?
23. The square ABCD is inscribed in a circle of radius . Find the shaded area. (Please see attached file)
24. A rectangle is 10 by 24. It is rotated about the shortest side. Find the volume of the cylinder. (Please see attached file)
26. One cubic inch of a certain iron weighs 8 ounces. A prism which measures 3 feet by 4 feet by 5 feet is made of that iron. How many pounds does it weigh?

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Solution Summary

We have the area of the square = a^2
Here the painting must be done to a total area containing 4 walls and the ceiling. Since the floor is rectangle, two walls will be of same area 120 by 9 square feet and remaining two will be of same area 96 by 9 square feet. Also the ceiling has an area equal to that of the floor, 120 by 96 square feet.
area of shaded portion = area of circle - area of square.
If r is the radius of the cylinder and h its height, then the volume of the cylinder.
Given that one cubic inch of a certain iron weighs 8 ounces.

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18. What is the area of a square if the length of a diagonal is 4 sq. rt. 2?

Solution: Let 'a' be the length of side of a square and 'd' be its diagonal length, then

Given length of a diagonal is . Then length of its side

We have the area of the square

22. The floor of a room is 120 feet by 96 feet. The ceiling is 9 feet above the floor. Everything is to be painted except the floor. (Don't worry about doors or windows). How many square yards must be painted?
NOTE: How many square feet in one square yard?

Solution: Here the painting must be done to a total area containing 4 walls and the ceiling. Since the floor is rectangle, two walls will be of same area 120 by 9 square feet and remaining two will be of same area 96 by 9 square ...

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