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mash [69]
2 years ago
12

A sphere is inscribed in a cube with a surface area of 216 square centimeters. What is the volume of the sphere

Mathematics
1 answer:
pentagon [3]2 years ago
7 0

Answer:

V=298.5cm^3

Step-by-step explanation:

To find the volume of the sphere we need to know its radius.

And the radius can be found with the information we have about the surface area.

The formula for the surface area is as follows:

SA=4\pi r^2

from this formula we clear the radius r:

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

and we substitute the known value of the surface area, and also the value of \pi:

r=\sqrt{\frac{216cm^2}{4(3.1416)} }\\ \\r=\sqrt{\frac{216cm^2}{12.5664} }\\ \\r=\sqrt{17.1887cm^2}\\ \\r=4.146cm

and now that we know the radius we find the volume:

V=\frac{4\pi r^3}{3} \\\\V=\frac{4(3.1416)(4.146cm)^3}{3}\\ \\V=\frac{895.521cm^3}{3}\\ \\V=298.5cm^3

the volume of the sphere is 298.5cm^3

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No idea how to do this equation. Its applying system's of linear equations.
icang [17]
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add 0.9y to both sides and you get:

x=4.5+0.9y

we now know what x is equal to in terms of y. so lets replace the x in the first equation with the new value. You get:

1.5(4.5+0.9y)-1.9y=-29

Now just solve for y:
6.75+1.35y-1.9y=-29
1.35y-1.9y=-35.75
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y=65

so now you know that y=65 so plug 65 in as y in the second equation to find x

x-0.9*65=4.5

Now simply solve for x

x-(-58.5)=4.5
x+58.5=4.5
x=-54

Hope this helped! :)



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3 years ago
What is the length of line segment dc
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Step-by-step explanation:

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Three consecutive even numbers have a sum where one half of the sum is between 84 and 96
mamaluj [8]

86 *2 = 172

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2 years ago
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