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julsineya [31]
3 years ago
10

3. The formula to find the surface area of a sphere is to take the radius of the sphere and square it and multiply that amount b

y pi and then multiply that by 4. This is written algebraically as S=4πr 2 , where S is the surface area, r is the radius, and the value of π is 3.14. Rewrite the equation to solve for the radius of the sphere if you know the sphere’s surface area. Then estimate the radius of a sphere given a surface area of 500 meters2 .
Mathematics
2 answers:
KatRina [158]3 years ago
6 0
The way to get the equation for the radius (r) is to get r by itself. So divide each side by 4pi
500/4pi=r^2
Now take the square root of each side to get the equation of r.
sqrt(500/4pi)=r
Bas_tet [7]3 years ago
5 0

Answer:

6.31 m

Step-by-step explanation:

The surface area (S) of a sphere is a function of its radius (r) according to the following expression.

S=4\pi r^{2}

We can rewrite it to solve for the radius given the surface area.

S=4\pi r^{2}\\r^{2} =\frac{S}{4\pi} \\r=\sqrt{\frac{S}{4\pi}}

When S = 500 m², the radius is

r=\sqrt{\frac{500m^{2} }{4\pi}}=6.31 m

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<u>Given:</u>

The rectangular prism has a length of 25 feet, a width of 10 feet and a height 55 feet.

The triangular prism has a base length of 25 feet, a height of 8 feet, and a prism height of 55 feet.

<u>To find:</u>

The total area to be painted.

<u>Solution:</u>

There are 4 external surfaces for the rectangular prism and 4 external surfaces for the triangular prism.

The rectangular prism has 4 rectangles out which there are 2 sets of similar rectangles.

There are two rectangles with lengths of 25 feet and widths of 10 feet while the other two rectangles have lengths of 55 feet and widths of 10 feet.

The area of a rectangle with a length of 25 feet and a width of 10 feet = 25(10)= 250 square ft.

The area of two such rectangles = 2(250) = 500 square feet.

The area of a rectangle with a length of 55 feet and a width of 10 feet = 55(10)= 550 square feet.

The area of two such rectangles = 2(550) = 1100 square feet.

The triangular prism has 2 triangles and 2 rectangles.

The triangles have base lengths of 25 feet and heights of 8 feet while the rectangles have lengths of 55 feet and heights of 14.8 feet.

The area of a triangle with a base length of 25 feet and a height of 8 feet = \frac{1}{2}(25)(8)= 100 square feet.

The area of two such triangles =2(100)= 200 square feet.

The area of a rectangle with a length of 55 feet and a width of 14.8 feet = 55(14.8)= 814 square feet.

The area of two such rectangles = 2(814) = 1628 square feet.

The total area to be painted =500+1100+200+1628 = 3128 square feet.

So an area of 3128 square feet is to be painted.

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