A cylindrical post has a cross section that is a circle with a radius of 3 inches. A piece of cord can be wound around it exactly seven times.How long is the piece of cord? Use 22/7 as the value of .
Answer(s): D
A length of cord that will wind around once is equal to the circumference of the circle whose radius is 3 inches.The circumference of a circle equals 2% r where n =22:7 and r is the radius.Circumference = 22/1 × 22/7 × 3/1 =132/7 inchesIf the cord can be wound around the post seven times, its length is seven times the length of one circumference.Length of cord 132/7 × 7/1 = 132 inches
A naval task force is to be made up of a destroyer, a supply ship, and a submarine.If four destroyers, two supply ships, and three submarines are available from which to choose, how many different combinations are possible for the task force?
Answer(s): B
There are four possible choices for the destroyer.Each of these choices may be coupled with any of the two choices for the supply ship.Each such destroyer-supply ship combination may in rum be coupled with any of the three possible choices for the submarine.Thus, there are 4 × 2 × 3, or 24, different combinations possible.
The base of a cylindrical can is a circle whose diameter is 2 inches. Its height is 7 inches.How many cubic inches are there in the volume of the can? Use 22/7 for the value of .
The volume of a cylinder is equal to the product of its height and the area of its base. The base is a circle. The area of a circle is r2, where = 22/7 and r is the radius. Since the diameter is 2 inches, the radius (which is one-half the diameter) is 1 inch.Area of circular base =22/7 × 1/1 × 1/1 = 22/7The height is 7 inches.22/7 × 7/1 = 22 cubic inches
A rectangular vegetable garden 16 yards long and 4 yards wide is completely enclosed by a fence. To reduce the amount of fencing used, the owner replaced the garden with a square one having the same area.How many yards of fencing did he save?
Answer(s): C
The area of the rectangular garden is equal to the product of its length and width. Area of rectangle = 16 × 4 = 64 square yards.In order for the square to have the same area, 64 square yards, its sides must each be 8 yards long, since 8 × 8 = 64 square yards. The fence around the rectangular garden has a length of 16 + 4 + 16 + 4, or 40, yards.The fence around the square garden has a length of 4 × 8, or 32, yards.The saving in fencing is 40 - 32, or 8, yards.
What is the maximum number of boxes, each measuring 3 inches by 4 inches by 5 inches, that can be packed into a storage space measuring 1 foot by 2 feet by 2 feet, 1 inch?
Answer(s): A
The storage space measurements of 1 foot by 2 feet by 2 feet, 1 inch can be converted to inches as 12 inches by 24 inches by 25 inches. Boxes measuring 3 inches by 4 inches by 5 inches can be stacked so that four of the 3-inch sides make up the 12-inch storage dimension, six of the 4-inch sides fill the 24-inch storage dimension, and five of the 5-inch sides fill the 25-inch storage dimension.There will be 4 × 6 × 5, or 120, boxes packed into the storage space.
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