The world's tallest building is the Burj Khalifa in Dubai at 828 m tall. The CN Tower in Toronto is 553 m tall. Ryan wants to compare the Burj Khalifa and the CN Tower by creating rectangular prism models on a 10 cm by 10 cm square base. He decided to represent the Burj Khalifa with a rectangular prism that has a height of 40 cm.
What is the volume of each rectangular prism? Round your answer to the nearest cubic centimeter.
Are your two models supposed to be in a ratio equal to the ratio of the height of the two buildings?
The buildings do not have the same shape, so we can't make a ratio comparison between their volumes.
The wording of the first two Related Questions below deal with the height, see the solutions for these
So,I have to find the height of the CN Tower then I can find the volume for the two rectangular prisms?
To find the volume of a rectangular prism, you need to multiply the length, width, and height.
For the Burj Khalifa model:
Length = 10 cm
Width = 10 cm
Height = 40 cm
Volume = Length * Width * Height
Volume = 10 cm * 10 cm * 40 cm
Volume = 4000 cm²
Therefore, the volume of the Burj Khalifa model is 4000 cubic centimeters.
Since we don't have the dimensions for the CN Tower model, we cannot calculate its volume.
To find the volume of a rectangular prism, you need to multiply the length, width, and height of the prism.
For the Burj Khalifa representation, the length and width of the base are both 10 cm. The height given is 40 cm.
Volume of Burj Khalifa representation = length × width × height
= 10 cm × 10 cm × 40 cm
= 4000 cm³
Therefore, the volume of the Burj Khalifa representation is 4000 cubic centimeters.
Now, let's move on to finding the volume of the CN Tower representation. The length and width of the base are again both 10 cm. However, we are not given the height of the CN Tower representation.
Since we know the actual height of the CN Tower is 553 m and the actual height of the Burj Khalifa is 828 m, we can set up a proportion to find the ratio between the heights of the two representations.
Let x represent the height of the CN Tower representation:
828 m (Burj Khalifa) / 40 cm (Burj Khalifa representation) = 553 m (CN Tower) / x cm (CN Tower representation)
Cross-multiplying gives:
828 m (Burj Khalifa) × x cm (CN Tower representation) = 553 m (CN Tower) × 40 cm (Burj Khalifa representation)
Simplifying further:
x = (553 m × 40 cm) / 828 m
x ≈ 26.7 cm
Therefore, the height of the CN Tower representation is approximately 26.7 cm.
Now we can calculate the volume of the CN Tower representation:
Volume of CN Tower representation = length × width × height
= 10 cm × 10 cm × 26.7 cm
= 2670 cm³
So, the volume of the CN Tower representation is 2670 cubic centimeters.