Two similar rectangular prisms have a scale factor of 4:9. The volume of the smaller prism is 60 cm3. Find the volume of the larger prism.
V = (9/4)^3 *60 =(729/64) * 60=683.4
cm3.
To find the volume of the larger prism, we can use the concept of scale factor.
The scale factor tells us the ratio of corresponding sides of the two similar shapes. In this case, the scale factor is 4:9.
Since the volume of a rectangular prism is determined by the length, width, and height, we can use the scale factor to relate the volumes of the two prisms.
The ratio of their volumes will be the scale factor cubed.
So, the volume of the larger prism is (4/9)^3 times the volume of the smaller prism.
Let's calculate it step by step:
Step 1: Find the scale factor cubed.
Scale factor = 4:9
=> Ratio = 4/9
=> Scale factor cubed = (4/9)^3
Step 2: Calculate the volume of the larger prism.
Volume of larger prism = (Scale factor cubed) * Volume of smaller prism
Volume of larger prism = (4/9)^3 * 60 cm^3
Step 3: Simplify the expression and calculate the final answer.
Volume of larger prism = (64/729) * (60 cm^3)
Volume of larger prism ≈ 4160/243 cm^3
Therefore, the volume of the larger prism is approximately 17.08 cm^3.
To find the volume of the larger prism, we'll need to use the scale factor of 4:9.
The scale factor tells us how many times larger the larger prism is compared to the smaller prism. In this case, the larger prism is 9/4 times larger than the smaller prism.
To find the volume of the larger prism, we'll need to multiply the volume of the smaller prism by the scale factor.
Volume of smaller prism = 60 cm^3
Scale factor = 4:9
Volume of larger prism = (Scale factor) * (Volume of smaller prism)
Volume of larger prism = (9/4) * (60 cm^3)
Now, let's calculate the volume of the larger prism.
Volume of larger prism = (9/4) * (60 cm^3)
Volume of larger prism = 540/4 cm^3
Volume of larger prism = 135 cm^3
Therefore, the volume of the larger prism is 135 cm^3.