A cube with a side length of 25m has a surface area of:

25m * 25m * 6 = 3,750 m2

(The surface area of a cube is equal to the area of one face of the cube multiplied by 6 sides. In other words, if the side of a cube is s, then the surface area of the cube is 6_s_2.)

Each square tile has an area of 5 m2.

Therefore, the total number of square tiles needed to fully cover the surface of the cube is:

3,750m2/5m2 = 750

Note: the volume of a cube with side length s is equal to _s_3. Therefore, if asked how many mini-cubes with side length n are needed to fill the original cube, the answer would be:

s3/n3

Write the surface area formula for a sphere.

Substitute the value of the radius.

Write the formula for the surface area of a cube.

Substitute the length.

The surface area of the prism can be broken into three rectangular sides and two equilateral triangular bases.

The area of the sides is given by: , so for all three sides we get .

The equilateral triangle is also an equiangular triangle by definition, so the base has congruent sides of 6 in and three angles of 60 degrees. We use a special right traingle to figure out the height of the triangle: 30 - 60 - 90. The height is the side opposite the 60 degree angle, so it becomes or 5.196.

The area for a triangle is given by and since we need two of them we get .

Therefore the total surface area is .

The surface area of the sphere before it was cut is equal to the following:

surface area of solid sphere = 4_πr_2, where r is the length of the radius.

Each hemisphere will have the following shape:

In order to determine the surface area of the hemisphere, we must find the surface area of the flat region and the curved region. The flat region will have a surface area equal to the area of a circle with radius r.

area of flat part of hemisphere = _πr_2

The surface area of the curved portion of the hemisphere will equal one-half of the surface area of the uncut sphere, which we established to be 4_πr_2.

area of curved part of hemisphere = (1/2)4_πr_2 = 2_πr_2

The total surface area of the hemisphere will be equal to the sum of the surface areas of the flat part and curved part of the hemisphere.

total surface area of hemisphere = _πr_2 + 2_πr_2 = 3_πr_2

Finally, we must find the ratio of the surface area of the hemisphere to the surface area of the uncut sphere.

ratio = (3_πr_2)/(4_πr_2) = 3/4

The answer is 3/4.

This problem is relatively simple. We know that the volume of a cube is equal to s3, where s is the length of a given side of the cube. Therefore, to find our dimensions, we merely have to solve s3 = 1728. Taking the cubed root, we get s = 12.

Since the sides of a cube are all the same, the surface area of the cube is equal to 6 times the area of one face. For our dimensions, one face has an area of 12 * 12 or 144 in2. Therefore, the total surface area is 6 * 144 = 864 in2.

Converting squared units is not difficult, though you have to be careful not to make a simple mistake. It is tempting to think you can merely multiply the initial value (24) by 36, as though you were converting from yards to inches.

Begin by thinking this through as follows. In the case of a single dimension, we know that:

1 yd = 36 in

Now, think the case of a square with dimensions 1 yd x 1 yd. This square has the following dimensions in inches: 36 in x 36 in. The area is therefore 36 * 36 = 1296 in2. This holds for all two-dimensional conversions. Therefore, the two dimensional conversion equation is:

1 yd2 = 1296 in2

Based on this, we can convert our value 24 yd2 thus: 24 * 1296 = 31,104 in2.

A cube has sides that have equal length edges and also equal side areas.

To find the total surface area, you just need to multiple the side area () by which is,

.

To find the surface area, we must first find the radius. Based on our description, this passes from (0,0) to (6,8). This can be found using the distance formula:

62 + 82 = _r_2; _r_2 = 36 + 64; _r_2 = 100; r = 10

It should be noted that you could have quickly figured this out by seeing that (6,8) is the hypotenuse of a 6-8-10 triangle (which is a multiple of the "easy" 3-4-5).

The rest is easy. The surface area of the sphere is defined by:

A = 4_πr_2 = 4 * 100 * π = 400_π_

To solve this, we must first begin by finding the radius of the sphere. To do this, recall that the volume of a sphere is:

V = (4/3)_πr_3

For our data, we can say:

2304_π_ = (4/3)_πr_3; 2304 = (4/3)_r_3; 6912 = 4_r_3; 1728 = _r_3; 12 * 12 * 12 = _r_3; r = 12

Now, based on this, we can ascertain the surface area using the equation:

A = 4_πr_2

For our data, this is:

A = 4_π_*122 = 576_π_