An artist wants to make alabaster pyramids using a block of alabaster with a volume of 576 cubic inches. She plans to make each pyramid with a square base area of 3 square inches and a height of 4 inches. At most, how many pyramids can the artist make from the block of alabaster?
The radii of Earth and Pluto are 6,371 kilometers and 1,161 kilometers, respectively. Approximately how many spheres the size of Pluto does it take to have the same volume as Earth?
To find out how many pyramids the artist can make from the block of alabaster, we need to determine the volume of each pyramid and then divide the total volume of the block by the volume of each pyramid.
The volume of a pyramid can be calculated using the formula:
Volume = (1/3) * base area * height
Given that the base area is 3 square inches and the height is 4 inches, we can substitute these values into the formula:
Volume = (1/3) * 3 * 4 = 4 cubic inches
The volume of each pyramid is 4 cubic inches.
To find out the maximum number of pyramids that can be made, we divide the volume of the block (576 cubic inches) by the volume of each pyramid (4 cubic inches):
Number of pyramids = 576 / 4 = 144
Therefore, the artist can make at most 144 pyramids from the block of alabaster.
To find out how many pyramids the artist can make from the block of alabaster, we need to calculate the total volume of each pyramid and then divide that by the volume of the block.
The volume of each pyramid can be calculated using the formula: volume = (1/3) * base area * height.
Given that the base area is 3 square inches and the height is 4 inches, we can substitute these values into the formula to calculate the volume of each pyramid.
volume = (1/3) * 3 square inches * 4 inches = 4 cubic inches.
Now, to find out how many pyramids the artist can make, we divide the volume of the block of alabaster by the volume of each pyramid.
Number of pyramids = volume of block of alabaster / volume of each pyramid
Number of pyramids = 576 cubic inches / 4 cubic inches = 144.
Therefore, the artist can make at most 144 pyramids from the block of alabaster.
Volume of alabaster= 576 in3
Length for base = 3 inches
Height= 4 inches
Volume of pyramid = lwh/3
= 3x3x4/3
= 12 in3
Number of pyramids that can be made from 576 in3 of alabaster = 576/12
= 48