The volume of a ball is 36 pi cm^3. Find the dimensions of a rectangular box that is large enough to hold the ball.

The box to hold the ball must be cubic, and each side is equal to the diameter, or twice the radius, r.

Volume of a sphere (ball)
= 4πr³/3 = 36 π
r³= 36*3/4 = 27
r = 3

So please continue to figure out the size of the box.

To find the dimensions of a rectangular box that can hold the ball, we need to determine the diameter of the ball.

The formula for the volume of a ball is given by:
V = (4/3) * π * r^3

We are given that the volume of the ball is 36π cm^3.

36π = (4/3) * π * r^3

We can cancel out π on both sides:

36 = (4/3) * r^3

To isolate r^3, we can multiply both sides by 3/4:

r^3 = (36 * 3) / 4
r^3 = 27

Taking the cube root of both sides, we find:

r = (cube root of 27)
r = 3 cm

The diameter of the ball is twice the radius, so:

d = 2 * r
d = 2 * 3
d = 6 cm

Now that we have the diameter of the ball, we can determine the dimensions of the rectangular box. Since the ball would be a snug fit, the dimensions of the box would be slightly larger than the diameter of the ball. Let's add 1 cm to each dimension.

Therefore, the dimensions of the rectangular box are:
Length = d + 1 = 6 + 1 = 7 cm
Width = d + 1 = 6 + 1 = 7 cm
Height = d + 1 = 6 + 1 = 7 cm

So, the dimensions of the rectangular box that can hold the ball are 7 cm x 7 cm x 7 cm.

To find the dimensions of the rectangular box that can hold the ball, we need to consider the dimensions of the ball itself.

The volume of a ball can be calculated using the formula V = (4/3) * π * r^3, where V represents the volume and r represents the radius of the ball.

In this case, we know the volume of the ball is 36π cm^3. Therefore, we can set up the equation:

36π = (4/3) * π * r^3

To simplify the equation, we can cancel out the π on both sides:

36 = (4/3) * r^3

To isolate r, we can divide both sides of the equation by (4/3):

(4/3) * r^3 = 36

r^3 = (36 * 3) / 4

r^3 = 27

To find the radius, we can find the cube root of both sides:

r = ∛27

r = 3

So, the radius of the ball is 3 cm.

Now, we can determine the dimensions of the rectangular box that can hold the ball. Since the ball is round, the dimensions of the rectangular box should be larger than the diameter of the ball.

The diameter of the ball is twice the radius, so the diameter is 2 * 3 = 6 cm.

Therefore, the dimensions of the rectangular box should be at least 6 cm in each dimension to accommodate the ball.