Surface Area and Volume of Spheres Question Please Help?

Question

I need help understanding these questions if you could explain with the answer so that I could see how you got there:

I know that Surface area formula is 4 Pie radius ^ 2
And volume is 4/3 Pie radius ^ 3

Find the diameter of a sphere that has a surface area of 169 pie in ^ 2.

Find the volume of a sphere with a radius of 17.3 inches in cubic feet to the nearest tenth of a cubic foot.

Find the volume, to the nearest cubic foot, of a sphere whose surface area is 100 ft ^ 2.

A sphere fits snugly inside a right cylinder as shown below. Find the volume lying outside the sphere but inside the cylinder to the nearest tenth of a cubic inch. Height of cylinder 2 inches and length is 5 inches.

Please help and explain.

Answer 1

If A = 4πr^2, then 169π in^2 = 4πr^2



I'm going to leave out units until the end.



169π = 4πr^2



Divide both sides by 4π.



169π/4π = r^2



Take the square root of both sides.



r = √(169π/4π)



Radius is half of the diameter, so multiply your radius by two.



Diameter = √(169π/4π) * 2 = 2√(169π/4π) in. or approximately 40.84 in.



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If 4/3πr^3 is the equation for the volume and you're given a radius with 17.3 inches, then...



V = 4/3π(17.3)^3

V = 4/3π(5177.717)

V = 6903.622667π cubic feet or approximately 21688.37 cubic feet



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You're given 100 ft^2 and you need to find volume. You're going to use the area formula to find the radius. Then you're going to plug in that radius into the volume formula.



100 = 4πr^2

100/4π = r^2

25π = r^2

r = √(25π) or 5√(π) ft.



V = 4/3π(5√(π))^3



Plug this into your calculator...



V = approximately 2915.57 cubic ft.



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I'd have to see the actual picture of the last problem to be sure, but my guess is that you find the volume of the sphere and the volume of the cylinder. You then take the volume of the cylinder minus the volume of the sphere to get the volume lying outside the sphere but inside the cylinder rounding to the nearest tenth.



Equation for volume of a cylinder: V = πr^3h



Hope this helps, and good luck!

Answer 2

In other words, the radius in the square root of the quotient, surface area over 4*pi. Ie, the square root of the quotient, 169*pi square inches over 4*pi. The quotient simplifies to 169/4 inches and this has an exact square root of 13/2 inches. Double this (the radius) to get the diameter.



Since a cubic foot is a cube with a side length of 12 inches, 12 cubic inches will fit along one edge, 144 (12 rows of 12) will cover one surface and 1728 (12 layers of 144) cubic inches will fill the cubic foot. Conversely, one cubic inch will be 1/1728 of a cubic foot. Using the formula as it is (without rearranging it) this time, the volume is 4/3 of pi multiplied by the cube of 17.3 inches. I don't know what this is but a calculator will tell you if you speak to it nicely. The result will be in cubic inches, so divide by 1728 to get the required multiple of the cubic foot. Alternatively, calculate 4/3 of pi multiplied by the cube of 17.3/12 feet.



The square of the volume is 16/9 pi^2 r^6. The cube of the surface area is 64 pi^3 r^6. Dividing the second of these equations by the first gives us A^3/V^2=64*9*pi/16, so A^3=36*pi*V^2. You can rearrange this and use A=100 square feet to find V.



The measurements you've given just aren't clear at all, but the volume inside the cylinder is pi*r^2*h, where r is the radius of each circular surface of the cylinder and h is their separation. Calculate this and whether it fits 'snugly' or not, deduct the volume of the sphere, 4/3*pi*R^3, where R is the radius (careful, not the diameter) of the sphere.

Answer 3

floor section Of Sphere = 4 Pi r^2 quantity of spere = 4/3 Pi r^3 a) radius doubled - floor section will grow to be sixteen time than till now quantity would be 8 situations extra. b)radius tripled - floor section will grow to be 36 situations of till now. and quantity would be 27 situations extra. b) multipled by using n . floor section would be n^2 situations extra and quantity would be n^three times extra