Find the missing measure for each pyramid
1)
area of base = 1,470 cm^2
volume= 22,050 cm^3
what is the height?______
I got 15cm^2
2) height = 26 feet
volume= 11,466 ft^3
what is the area of the base?_____
I got 441 ft^2
Thank you!
1)
Volume = (1/3)*h*A
=> h = (V*3)/A
=> h = (22050*3)/1470
= 45 cm
Your numerical value is incorrect, but additionally, how do you get square centimeters for a distance?
2)
Volume = (1/3)*h*A
=> A = (V*3)/h
= (11466*3)/26
= 1323 ft^2
The answer you got in both cases is exactly one third of the actual answer, have you used the correct formula?
To find the missing measures for the given pyramids, we can use the formulas for the volume and area of a pyramid. Let's go through each question step by step:
1) For the first pyramid, we are given the area of the base (1,470 cm^2) and the volume (22,050 cm^3). We need to find the height of the pyramid.
The formula for the volume of a pyramid is:
Volume = (1/3) * base area * height
So, we can rearrange the formula to solve for the height:
height = Volume / ((1/3) * base area)
Plugging in the given values, we have:
height = 22,050 cm^3 / ((1/3) * 1,470 cm^2)
Simplifying the expression on the denominator:
height = 22,050 cm^3 / (1/3 * 1,470 cm^2)
height = 22,050 cm^3 / (1/3 * 1,470 cm^2)
height = 22,050 cm^3 / (490 cm^2)
height = 45 cm
So, the height of the pyramid is 45 cm, not 15 cm^2 as you mentioned.
2) For the second pyramid, we are given the height (26 feet) and the volume (11,466 ft^3). We need to find the area of the base.
The formula for the volume of a pyramid is the same as before:
Volume = (1/3) * base area * height
Using the given values, we can rearrange the formula to solve for the base area:
base area = Volume / ((1/3) * height)
Plugging in the values:
base area = 11,466 ft^3 / ((1/3) * 26 ft)
Simplifying the denominator:
base area = 11,466 ft^3 / (1/3 * 26 ft)
base area = 11,466 ft^3 / (8.67 ft)
base area ≈ 1,324.5 ft^2
So, the area of the base for the second pyramid is approximately 1,324.5 ft^2, not 441 ft^2 as you mentioned.
Therefore, the correct answers are:
1) The height of the pyramid is 45 cm.
2) The area of the base is approximately 1,324.5 ft^2.