Answer:
B.144
Step-by-step explanation:
Given :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.
To Find: At most, how many pyramids can the artist make from the block of alabaster?
Solution:
Formula of volume of square pyramid:
[tex]\frac{a^{2}h}{3}[/tex]
Where a is the base length of the square base of the square pyramid.
h is the height of the square pyramid.
Since we are given a square base area of 3 square inches and a height of 4 inches.
⇒[tex]a^{2}=3[/tex]
⇒[tex]h=4[/tex]
Volume of pyramid that artist make :
[tex]\frac{3*4}{3}[/tex]
[tex]\frac{12}{3}[/tex]
[tex]4[/tex]
Thus volume of 1 square pyramid is 4 cubic inches.
Volume of alabaster pyramid is 576 cubic inches
To calculate At most, how many pyramids can the artist make from the block of alabaster
Volume of alabaster pyramid/ volume of 1 square pyramid
⇒[tex]\frac{576}{4}[/tex]
⇒[tex]144[/tex]
Thus the artist can make 144 pyramids from the block of alabaster.
Hence option B is correct.
