Volumen of A Solid
Given a solid with a shape of a constant base B and height H, the volume is:
V = BH
The height of the solid is 1 1/4 ft. We need to calculate the area of the base.
The base consists of a larger rectangle from which has been taken a smaller rectangle.
The larger rectangle has dimensions of 9 ft by 6 ft, thus its area is:
A1 = 9 ft * 6 ft = 54 square ft
The smaller rectangle has dimensions of 2 1/2 ft by 4 ft.
The second dimension was calculated as the difference between 9 ft and 2 ft plus 3 ft. (9 ft - 3 ft - 2 ft = 4 ft).
The area of the smaller rectangle is:
A2 = 2 1/2 * 4
The mixed fraction 2 1/2 is converted to improper fraction:
2 1/2 = 2 + 1/2 = 5/2
Thus, the area is:
A2 = 5/2 * 4
A2 = 10 square feet
The area of the base is A1 - A2 = 54 square feet - 10 square feet = 44 square feet
B = 44 square feet.
Now for the volume:
V = 44 square feet * 1 1/4 feet
Again the mixed fraction is converted to a single fraction:
1 1/4 = 1 + 1/4 = 5/4
V = 44 square feet * 5/4 feet
V = 55 cubic feet
1) The outcomes for rolling two dice, the sample space, is as follows:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
There are 36 outcomes in the sample space.
2) The ways to roll an odd sum when rolling two dice are:
(1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (3, 6), (4, 1), (4, 3), (4, 5), (5, 2), (5, 4), (5, 6), (6, 1), (6, 3), (6, 5). There are 18 outcomes in this event.
3) The probability of rolling an odd sum is 18/36 = 1/2 = 0.5
