PLEASE HELP ASAP!!!
1 rectangular prism has a base area of 120 square feet, a height of 12 feet per second and has dimensions of 84 inches, 6 feet, and 16 feet. Is the volume of the second more than or less than half that of the first?
now explain
Your post makes absolutely no sense to me.
"a height of 12 feet per second " ????
are there two prisms ?
Just guessing now:
If one prism has a base area of 120 ft^2, and a height of 12 ft, then its volume is
1440 cubic feet
if a second prism is 84 inches by 6 ft by 16 ft
or 7ft by 6ft by 16ft, it would have a volume of
672 cubic ft
so what is half of the first?
compare that to the second.
Half
To determine if the volume of the second rectangular prism is more or less than half that of the first, we need to calculate the volumes of both prisms and compare them.
First, let's convert the dimensions of the first prism from inches to feet:
- Length: 84 inches = 84/12 = 7 feet
- Width: 6 feet (already in feet)
- Height: 16 feet (already in feet)
The volume of the first prism can be found by multiplying the base area by the height:
Volume of the first prism = Base area * Height
= 120 square feet * 12 feet
= 1440 cubic feet
Now, let's move on to the second prism. Its dimensions are already in feet:
- Length: 84 feet (already in feet)
- Width: 6 feet (already in feet)
- Height: 16 feet (already in feet)
Similarly, the volume of the second prism can be calculated:
Volume of the second prism = Base area * Height
= 120 square feet * 12 feet
= 1440 cubic feet
Comparing the volumes:
- Volume of the second prism = 1440 cubic feet
- Half the volume of the first prism = 1/2 * 1440 cubic feet = 720 cubic feet
Since the volume of the second prism (1440 cubic feet) is greater than half the volume of the first prism (720 cubic feet), we can conclude that the volume of the second rectangular prism is more than half that of the first.
To find out if the volume of the second rectangular prism is more or less than half of the volume of the first, we need to calculate the volumes of both prisms and compare them.
Let's start with the first rectangular prism. We are given the base area of 120 square feet and the height of 12 feet. To find the volume, we multiply the base area by the height:
Volume of the first rectangular prism = base area * height
Since the base area is given in square feet, we need to convert the height to feet as well:
Volume of the first rectangular prism = 120 sq ft * 12 ft
To multiply these values, we need to convert the base area from square feet to square inches because the dimensions of the second prism are given in inches. There are 12 inches in a foot, so we can convert the base area as follows:
120 sq ft = 120 sq ft * (12 inches/1 foot)^2
= 120 sq ft * (12 inches)^2
= 120 sq ft * 144 square inches
= 17,280 square inches
Now we can calculate the volume of the first rectangular prism:
Volume of the first rectangular prism = 17,280 square inches * 12 ft
Next, let's calculate the volume of the second rectangular prism. We are given its dimensions as 84 inches, 6 feet, and 16 feet. To find the volume, we multiply the length, width, and height:
Volume of the second rectangular prism = length * width * height
To make the units consistent, we need to convert all the dimensions to inches:
Length = 84 inches
Width = 6 ft * 12 inches/ft = 72 inches
Height = 16 ft * 12 inches/ft = 192 inches
Now we can calculate the volume of the second rectangular prism:
Volume of the second rectangular prism = 84 inches * 72 inches * 192 inches
Finally, we can compare the volumes of the two prisms. If the volume of the second prism is more than half of the volume of the first prism, we can say that the volume of the second prism is more. If it is less than half, we can say it is less.
Calculate the volumes of the two prisms using the formulas and conversions above, and then compare them to determine the answer to the question.