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!
volume of pyramid is 1/3 the product of the area of the base and the height
v = 1/3 * (base area) * height
looks like you left out the 1/3
To find the missing measure for each pyramid, you can use the formulas for the volume and area of the base. Let's solve each problem step by step:
1) In this problem, you are given the area of the base and the volume of the pyramid, and you need to find the height. The formula for the volume of a pyramid is given by V = (1/3) * A_base * height, where V is the volume, A_base is the area of the base, and height is the height of the pyramid.
Given that V = 22,050 cm^3 and A_base = 1,470 cm^2, we can plug in these values into the formula and solve for the height:
22,050 = (1/3) * 1,470 * height
To get the height, we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by 3 and dividing by 1,470:
(22,050 * 3) / 1,470 = height
Calculating the right side of the equation, we find that the height is approximately 45 cm.
So, the missing measure for this pyramid is the height, which is approximately 45 cm.
2) In this problem, you are given the height and the volume of the pyramid, and you need to find the area of the base. The formula for the volume of a pyramid is still V = (1/3) * A_base * height.
Given that V = 11,466 ft^3 and height = 26 feet, we can rearrange the formula to solve for the area of the base:
A_base = (3 * V) / (height)
Plugging in the given values, we get:
A_base = (3 * 11,466) / 26
Calculating the right side of the equation, we find that the area of the base is approximately 441 ft^2.
So, the missing measure for this pyramid is the area of the base, which is approximately 441 ft^2.
Therefore, the answers to the two problems are:
1) The height is approximately 45 cm.
2) The area of the base is approximately 441 ft^2.