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 your answer in terms of pi.(1 point)%0D%0A6 in2
To find the largest size sphere that can fit inside the box, we need to determine the diameter of the sphere.
The diameter of the sphere is equal to the shortest side length of the box, which in this case is 12 inches.
The surface area of a sphere with diameter d is given by the formula:
Surface Area = 4πr^2
where r is the radius of the sphere.
Since the diameter is 12 inches, the radius is half of the diameter, which is 6 inches.
Substituting the value of the radius into the formula, we get:
Surface Area = 4π(6)^2 = 4π(36) = 144π square inches.
Therefore, the surface area of the largest size sphere that can fit in the box is 144π square inches.
just inches
Apologies for the confusion. The surface area of the largest size sphere that can fit in the box is 144 square inches.
not square inches inches
Apologies for the confusion once again. The largest size sphere that can fit in the box would have a diameter equal to the shortest side length of the box, which is 12 inches. Therefore, the surface area of the largest size sphere would be:
Surface Area = 4πr²
= 4π(6)²
= 144π square inches.
So, the surface area of the largest size sphere that can fit in the box is 144π square inches.
To find the surface area of the largest size sphere that can fit inside a rectangular box, we need to determine the diameter of the sphere.
In this case, the dimensions of the box are given as 12 inches, 14 inches, and 18 inches. To find the diameter, we need to determine the shortest side of the box since the sphere can fit snugly in the smallest dimension.
The shortest side of the box is 12 inches. Therefore, the diameter of the largest size sphere that can fit inside the box is also 12 inches.
The surface area of a sphere can be calculated using the formula: SA = 4πr^2, where SA is the surface area and r is the radius of the sphere.
Since we have the diameter (d = 12 inches), we can find the radius (r) by dividing the diameter by 2:
r = d/2 = 12/2 = 6 inches
Now, we can calculate the surface area of the sphere using the formula:
SA = 4πr^2 = 4π(6^2) = 4π(36) = 144π
Therefore, the surface area of the largest size sphere that can fit inside the given box is 144π square inches.