To find the radius of a cylinder that holds the same volume of cereal as the rectangular prism, we first need to use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
Where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
We know that the volume \( V \) is 420 cubic inches and the height \( h \) is 4 inches. We need to solve for the radius \( r \):
\[ 420 = \pi r^2 \cdot 4 \]
First, isolate \( r^2 \) by dividing both sides by \( 4\pi \):
\[ r^2 = \frac{420}{4\pi} \]
\[ r^2 = \frac{420}{4\pi} \]
\[ r^2 = \frac{420}{4 \times 3.14159} \]
\[ r^2 = \frac{420}{12.56636} \]
\[ r^2 \approx 33.42 \]
Now, take the square root of both sides to find \( r \):
\[ r \approx \sqrt{33.42} \]
\[ r \approx 5.78 \]
Rounding to the nearest whole number, the radius is approximately 6 inches.
So, the redesigned package should have a radius of 6 inches, making the correct answer:
6 inches
6. A family-size cereal box in the shape of a rectangular prism with dimensions of 14 in x 10 in x 3 in holds 420 cubic inches of cereal.
If the packaging is redesigned to be a cylinder with a height of 4 inches, what would be the approximate radius so that it still holds the same volume of cereal?
(Round to the nearest whole number.)
4 inches
5 inches
6 inches
7 inches
1 answer
3 answers