The fomula for the volume of a cone is

Because our radius of the base is , we know that .

.

Here we simply need to remember the formula for the surface area of a cone and plug in our values for the radius and height.

Lateral Area = LA = π(r)(l) where r = radius of the base and l = slant height

LA = 2B

π(r)(l) = 2π(r²)

rl = 2r²

l = 2r

From the diagram, we can see that r² + h² = l².  Since h = 9 and l = 2r, some substitution yields

r² + 9² = (2r)² 

r² + 81 = 4r² 

81 = 3r² 

27 = r²

B = π(r²) = 27π

LA = 2B = 2(27π) = 54π

SA = B + LA = 81π

We need to find total surface area of the cone and the area of the base. 

The area of the base of a cone is equal to the area of a circle. The formula for the area of a circle is given below:

, where r is the length of the radius.

In the case of this cone, the radius is equal to 4R, so we must replace r with 4R.

To find the total area of the cone, we need the area of the base and the lateral surface area of the cone. The lateral surface area (LA) of a cone is given by the following formula:

, where r is the radius and l is the slant height. 

We know that r = 4R. What we need now is the slant height, which is the distance from the edge of the base of the cone to the tip. 

In order to find the slant height, we need to construct a right triangle with the legs equal to the height and the radius of the cone. The slant height will be the hypotenuse of this triangle. We can use the Pythagorean Theorem to find an expression for l. According to the Pythagorean Theorem, the sum of the squares of the legs (which are 4R and 3R in this case) is equal to the square of the hypotenuse (which is the slant height). According to the Pythagorean Theorem, we can write the following equation:

Let's go back to the formula for the lateral surface area (LA).

To find the total surface area (TA), we must add the lateral area and the area of the base.

The problem requires us to find the ratio of the total surface area to the area of the base. This means we must find the following ratio:

We can cancel , which leaves us with 36/16.

Simplifying 36/16 gives 9/4.

The answer is 9/4.

The volume of a cubic box is given by (side length)³. Thus, the volume of the larger box is (4x)³ = 64x³, while the volume of the smaller box is x³. Divide the volume of the larger box by that of the smaller box, (64x³)/(x³) = 64.

Determine the volume of both cubes and then subtract the smaller from the larger.  The large cube volume is 9” * 9” * 9” = 729 in³ and the small cube is 3” * 3” * 3” = 27 in³.  The difference is 702 in³.

A cube that has three times as long sides is 3x3x3=27 times bigger than the original. Therefore, the answer is 5x27= 135.

Using S as the side length in the original cube, the original is s*s*s. Doubling one side and tripling the other gives 2s*2s*2s for a new volume formula for 8s*s*s, showing that the new volume is 8x greater than the original.

Cubes have 6 faces. If 2 are red, then 4 must be green. We are told that the total area of the green faces is 36 square inches, so we divide the total area of the green faces by the number of green faces (which is 4) to get the area of each green face: 36/4 = 9 square inches. Since each of the 6 faces of a cube have the same size, we know that each edge of the cube is √9 = 3 inches. Therefore the volume of the cube is 3 in x 3 in x 3 in = 27 cubic inches.

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.