The volume of the box is 50 * 20 * 30 cm = 30,000 cm³.

1cm³ = 1mL, 30,000 cm³ = 30,000mL = 30 L.

Because the volume of the box is only 30 L, 5 L of the 35 L will not fit into the box.

She will stack 360 bales in 3 hours. One row requires 15 bales. 360 divided by 15 is 24. 

The volume of a cube is .

If each side of the cube is , then the volume will be .

If we double each side, then each side would be and the volume would be .

There surface are of a cube is 6 times the area of one face of the cube , therefore

a is equal to an edge of the cube

the volume of the cube is

The problem states that the dimensions of the smaller boxes are 1 x 5 x 5, the volume of one of the smaller boxes is 25.

Therefore, 125/25 = 5 small boxes

A cubic volume is . Let the original sides be 1, so that the original volume is 1. Then find the volume if the sides measure 5.  This new volume is 125.  Therefore, the ratio of new volume to old volume is 125: 1.

To make this problem easier to solve, we can inscribe a smaller square in the cube.  In the diagram above, points  are midpoints of the edges of the inscribed cube.  Therefore point , a vertex of the smaller cube, is also the center of the sphere.  Point  lies on the circumference of the sphere, so .   is also the hypotenuse of right triangle .  Similarly,  is the hypotenuse of right triangle .  If we let , then, by the properties of a right triangle, .

Using the Pythagorean Theorem, we can now solve for :

Since the side of the inscribed cube is , the volume is .

Volume is calculated by height x width x length: 

For a cube, the height, width, and length are all the same value, so the equation can be simplified to , where  is the length of one edge of the cube.

We know that for the initial cube, , so we can substitute this into the volume equation and solve for the length of one of the cube's sides:

So, one edge of the initial cube is  long. When doubled, the cube will have edges that are each  long. We can solve for the final volume of the cube by substituting  into the equation for the volume of a cube and solving:

The volume of a cone is given by the formula V = (πr²)/3. In order to determine how many seconds it will take for the tank to fill, we must divide the volume by the rate of flow of the water.

time in seconds = (πr²)/(3w)

In order to convert from seconds to minutes, we must divide the number of seconds by sixty. Dividing by sixty is the same is multiplying by 1/60.

(πr²)/(3w) * (1/60) = π(r²)(h)/(180w)

The basic form for the volume of a cone is:

V = (1/3)πr²h

For this simple problem, we merely need to plug in our values:

V = (1/3)π13² * 6 = 169 * 2π = 338π in³

There are two things to be careful with here.  First, we must solve for the radius of the base. Secondly, note that the height is given in feet, not inches. Notice that all the answers are in cubic inches. Therefore, it will be easiest to convert all of our units to inches.

First, solve for the radius, recalling that C = 2πr, or, for our values 77π = 2πr. Solving for r, we get r = 77/2 or r = 38.5.

The height, in inches, is 24.

The basic form for the volume of a cone is: V = (1 / 3)πr²h

For our values this would be:

V = (1/3)π * 38.5² * 24 = 8 * 1482.25π = 11,858π in³