A rectangular box is 12 in. * 14 in. * 18 in. What is the surface area of the largest size sphere that could fit in this box? leave you answer in terms of pi? In this case pi would be 3.14
To fit the largest possible sphere inside a rectangular box, the sphere's diameter must be equal to the smallest dimension of the box, because the sphere must fit within the box in every direction.
Since the dimensions of the box are 12 inches, 14 inches, and 18 inches, the smallest dimension is 12 inches. That means the diameter of the largest sphere that can fit inside the box is also 12 inches.
The radius of the sphere is half of the diameter, so:
\[
r = \frac{d}{2} = \frac{12\ \text{inches}}{2} = 6\ \text{inches}
\]
The formula for the surface area of a sphere is:
\[
A = 4\pi r^2
\]
Plugging in the radius and the approximation for pi (3.14), we get:
\[
A = 4\cdot 3.14 \cdot (6\ \text{inches})^2
\]
\[
A = 4\cdot 3.14 \cdot 36\ \text{in}^2
\]
\[
A = 12.56 \cdot 36\ \text{in}^2
\]
\[
A = 452.16\ \text{in}^2
\]
Therefore, the surface area of the largest size sphere that could fit in the box, using the approximation of pi as 3.14, would be 452.16 square inches. If you want the answer in terms of pi exactly, it would be:
\[
A = 4\pi (6\ \text{inches})^2
\]
\[
A = 4 \cdot \pi \cdot 36\ \text{in}^2
\]
\[
A = 144\pi\ \text{in}^2
\]