Review
Pyramid A is a right square pyramid with a height of 66 m and a square base with a perimeter of 324 m . Pyramid B has a square base with a perimeter of 224 m and a height
pyramid has the greater volume and by how many times as great?
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The volume of pyramid B is times greater than the volume of pyramid A .
(Round to the nearest tenth as needed.)
B. The volume of pyramid A is times greater than the volume of pyramid B . 15.82 of 24 points
(Round to the nearest tenth as needed.)
C. The two pyramids have equal volume.

Question

Review
Pyramid A is a right square pyramid with a height of 66 m and a square base with a perimeter of 324 m . Pyramid B has a square base with a perimeter of 224 m and a height
pyramid has the greater volume and by how many times as great?
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The volume of pyramid B is

times greater than the volume of pyramid A .
(Round to the nearest tenth as needed.)
B. The volume of pyramid A is

times greater than the volume of pyramid B . 15.82 of 24 points
(Round to the nearest tenth as needed.)
C. The two pyramids have equal volume.

UpStudy AI · Accepted Answer

To find the volume of a pyramid, we use the formula:

$$ V = \frac{1}{3}Bh $$

where:
- $$ V $$ is the volume of the pyramid,
- $$ B $$ is the area of the base of the pyramid, and
- $$ h $$ is the height of the pyramid.

Given:
- Pyramid A: Height = 66 m, Perimeter of the base = 324 m
- Pyramid B: Perimeter of the base = 224 m

First, we need to find the area of the base for each pyramid.

For Pyramid A:
- The perimeter of the base is 324 m, so the side length of the base is $$ \frac{324}{4} = 81 $$ m.
- The area of the base is $$ 81^2 = 6561 $$ m².

For Pyramid B:
- The perimeter of the base is 224 m, so the side length of the base is $$ \frac{224}{4} = 56 $$ m.
- The area of the base is $$ 56^2 = 3136 $$ m².

Now, we can calculate the volume of each pyramid using the formula:

For Pyramid A:
$$ V_A = \frac{1}{3} \times 6561 \times 66 $$

For Pyramid B:
$$ V_B = \frac{1}{3} \times 3136 \times 66 $$

Let's calculate the volumes of the pyramids and then compare them to determine which pyramid has the greater volume and by how many times as great.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1}{3}\times 6561\times 66$$
- step1: Multiply the terms:
  $$2187\times 66$$
- step2: Multiply the numbers:
  $$144342$$
Calculate or simplify the expression $$ (1/3)*3136*66 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1}{3}\times 3136\times 66$$
- step1: Multiply the terms:
  $$\frac{3136}{3}\times 66$$
- step2: Reduce the numbers:
  $$3136\times 22$$
- step3: Multiply the numbers:
  $$68992$$
The volume of Pyramid A is 144342 cubic meters, and the volume of Pyramid B is 68992 cubic meters.

Since 144342 is greater than 68992, Pyramid A has a greater volume.

To find out by how many times as great the volume of Pyramid A is compared to Pyramid B, we divide the volume of Pyramid A by the volume of Pyramid B:

$$ \frac{144342}{68992} \approx 2.09 $$

Therefore, the volume of Pyramid A is approximately 2.09 times greater than the volume of Pyramid B.

So, the correct answer is:
A. The volume of pyramid B is $$ \boxed{2.09} $$ times greater than the volume of pyramid A.
Pyramid A has a volume approximately 2.09 times greater than Pyramid B.

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