The surface area of a sphere is 4πr². The area of a circle is πr². 16/16 is equal to 1.

Let's call the radius of the sphere r. The formula for the surface area of a sphere (A) is given below:

A = 4πr²

Because the sphere is inscribed inside the cube, the diameter of the sphere is equal to the side length of the cube. Because the diameter is twice the length of the radius, the diameter of the sphere is 2r. This means that the side length of the cube is also 2r. 

The surface area for a cube is given by the following formula, where s represents the length of each side of the cube:

surface area of cube = 6s²

The formula for surface area of a cube comes from the fact that each face of the cube has an area of s², and there are 6 faces total on a cube. 

Since we already determined that the side length of the cube is the same as 2r, we can replace s with 2r.

surface area of cube = 6(2r)² = 6(2r)(2r) = 24r².

We are asked to find the ratio of the surface area of the cube to the surface area of the sphere. This means we must divide the surface area of the cube by the surface area of the sphere.

ratio = (24r²)/(4πr²)

The r² term cancels in the numerator and denominator. Also, 24/4 simplifes to 6.

ratio = (24r²)/(4πr²) = 6/π

The answer is 6/π.

A hemisphere is half of a sphere.  The surface area is broken into two parts:  the spherical part and the circular base. 

The surface area of a sphere is given by $\displaystyle SA = 4\pi r^{2}$.

So the surface area of the spherical part of a hemisphere is $\displaystyle SA = 2\pi r^{2}$. 

The area of the circular base is given by $\displaystyle A = \pi r^{2}$.  The radius to use is half the diameter, or 2 cm.

Write the surface area formula for a sphere.

$\displaystyle A=4\pi r^2$

Substitute the value of the radius.

$\displaystyle A=4\pi r^2= 4\pi (10)^2 = 400 \pi$

Write the formula for the surface area of a cube.

$\displaystyle S=6s^2$

Substitute the length.

$\displaystyle S=6(10)^2= 600$

Write the formula for the surface area of a cube.

$\displaystyle A= 6s^2$

Substitute the side length into the equation.

$\displaystyle A= 6(3)^2$

Simplify the square inside the parentheses and multiply.

$\displaystyle A= 6(3)^2 = 6\times 9= 54$

To solve, simply use the following formula for the surface area of a cube.

Thus,

$\displaystyle \\SA=6s^2\\SA=6*(2x)^2\\SA=6*4x^2\\SA=24x^2$

A cube has $\displaystyle 6$ 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 ($\displaystyle 25$) by $\displaystyle 6$ which is,

$\displaystyle \\SA=6\cdot A \\SA=6\cdot 25 \\SA=150$.

The radius of a sphere is half its diameter, which here is 12, so the radius is 6. The surface area of the sphere can be calculated by setting $\displaystyle r = 6$ in the formula:

$\displaystyle A = 4 \pi r^{2}$

$\displaystyle A = 4 \pi \cdot 6^{2}$

$\displaystyle A = 4 \pi \cdot 36$

$\displaystyle A = 144 \pi$

75% of this is

$\displaystyle 144 \pi \cdot \frac{75}{100} = 108 \pi$

The surface area of the cylinder can be calculated by setting $\displaystyle r = 20$ and $\displaystyle h = 30$ in the formula

$\displaystyle A =2 \pi r (r + h)$

$\displaystyle A =2 \pi \cdot 20 (20 + 30)$

$\displaystyle A =2 \pi \cdot 20 \cdot 50$

$\displaystyle A = 2,000 \pi$

40% of this surface area is

$\displaystyle 2 ,000 \pi \cdot \frac{40}{100} = 800 \pi$