If a sphere has a volume of 3487 cubic yards whats the radius?

Answer 1

#" "#
Radius of the Sphere #~~color(red)(" 9.4 yards"#

#" "#
Volume of a Sphere (V) Formula: #color(blue)((4/3) * pi * r^3#

Given: #color(brown)(Volume (V) = "3487 Cubic yards"#

Find the Radius (r) using the formula.

Substitute the values known:

#3487=(4/3)*pi*r^3#

Mathematical Constant #color(blue)(pi# has an approximate value of 3.14159

#rArr 3487 = (4/3)*3.14159*r^3#

Switch sides:

#rArr (4/3)*3.14159*r^3 = 3487#

Divide both sides by #4/3#

#rArr [(4/3)*3.14159*r^3]/(4/3) = 3487/(4/3)#

Simplify:

#rArr [cancel(4/3)*3.14159*r^3]/cancel(4/3) = 3487/(4/3)#

#rArr 3.14159*r^3 = 3487/(4/3)#

Divide both sides by #3.14159#

#rArr (3.14159*r^3)/3.14159 = 3487/((4/3)*3.14159)#

Simplify:

#rArr [(cancel(3.14159)*(r^3))/cancel3.14159] = 3487/((4/3)*3.14159)#

#rArr r^3 = 3487/((4/3)*3.14159)#

Using calculator:

#r^3 ~~ 3487/4.188790205 #

#r^3 ~~ 832.45993#

#r~~832.45993^(1/3)#

Using a calculator:

#r~~ 9.407071523#

Hence,

Radius of the Sphere #~~color(red)(" 9.4 yards"#

Hope it helps.

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Answer 2

To find the radius of a sphere when given its volume, you can use the formula for the volume of a sphere:

[ V = \frac{4}{3} \pi r^3 ]

Given that the volume of the sphere is ( 3487 ) cubic yards, we can rearrange the formula to solve for the radius:

[ r^3 = \frac{3V}{4\pi} ]

[ r = \sqrt[3]{\frac{3V}{4\pi}} ]

Substitute the given volume ( V = 3487 ) cubic yards into the formula:

[ r = \sqrt[3]{\frac{3 \times 3487}{4\pi}} ]

Calculate:

[ r = \sqrt[3]{\frac{10461}{4\pi}} ]

[ r \approx \sqrt[3]{\frac{10461}{12.5664}} ]

[ r \approx \sqrt[3]{832.5} ]

[ r \approx 9.541 ]

So, the radius of the sphere is approximately ( 9.541 ) yards.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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