Source: ChinaTrip2005-110, Bobak Ha’Eri, Wikimedia Commons

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Keith's Plan ►

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The Giant Wild Goose Pagoda in Xi’an, China, is a 65-meter tall structure composed of a sequence of right rectangular prisms with square bases resting

on a concrete pedestal.

 

The bottom prism of the pagoda is a square with a side length of 33.5 meters. The top prism of the pagoda is a square with a side length of 12.2 meters. Each prism has the same height, which is 9.3 meters.

 

How much more volume does the bottom prism

have than the top prism?

The bottom prism has a square base. The length and width of the square are both 33.5 meters, and the height of the prism is 9.3 meters. The top prism has a square base. The length and width of the square are both 12.2 meters, and the height of the prism is 9.3 meters.

What are you given?
What does the problem ask for?
The problem asks for the difference between the volume of the top prism and the bottom prism.
Step 2: Make a plan.
What is your plan to solve this problem?

Keith's Plan

 

The volume of a prism can be found using the formula, V = Bh, where B represents the area of the base and h represents the height of the prism. These are square prisms, so I’ll use the area formula of a rectangle, A = bh, to calculate the area of the base of the prism. Then, I can subtract the volumes of the two prisms to determine the difference in their volumes.

What area formula(s) do you need to use?

Use the volume formula for a prism, V = Bh. Since the base is a square, use the area formula for a rectangle, A = bh since a square is a special type of rectangle..

Step 1: Understand the problem.

Write an equation that you could use to calculate the area of one stained glass window.

Top prism: V = (12.2 meters)(12.2 meters)(9.3 meters)

 

Bottom prism: V = (33.5 meters)(33.5 meters)(9.3 meters)

Step 3: Implement the plan.

Volume of the top prism:

V = (12.2 m)(12.2 m)(9.3 m)

= 1384.212 m3

 

Volume of the bottom prism:

V = (33.5 m)(33.5 m)(9.3 m)

= 10,436.925 m3

 

Difference:

10,436.925 m3 – 1384.212 m3

= 9052.713 m3

Step 4: Check your answer for reasonableness.

Strategy check: Use rounding to estimate your answer. Round 12.2 meters, 33.5 meters, and 9.3 meters to the nearest 10 meters.

12.2 meters → 10 meters

 

33.5 meters → 30 meters

 

9.3 meters → 10 meters

Use the estimated values to calculate an approximate area of one window and then ten windows.

Volume of the top prism: V ≈ (10 m)(10 m)(10 m)= 1,000 m3

 

Volume of the bottom prism: V ≈ (30 m)(30 m)(10 m)= 9,000 m3


Difference: 9,000 m3 - 1,000 m3 = 8,000 m3

Compare your estimate to your actual answer.

The estimate of 8,000 m3 is close to the actual answer of 9052.713 m3, so the answer is reasonable.