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? a.136 b.144 c.154 d.166 e.172

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:

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.

⇒

⇒

Volume of pyramid that artist make :

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

⇒

⇒

Thus the artist can make 144 pyramids from the block of alabaster.

Hence option B is correct.

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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