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How do you find the volume of the sphere in terms of #pi# given #V=4/3pir^3# and d=10cm?

Answer 1

Aurora Ayala

The volume of the sphere in terms of #pi# is #(500pi)/3# #cm^3#

#d=10# #cm.# means diameter is #10# #cm.# and hence the radius #r#, being half the diameter is #10/2=5# #cm.#

Hence, the volume of the sphere #V=4/3pir^3=4/3pixx5^3#

= #4/3pixx125#

= #(500pi)/3# #cm^3#

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Answer 2

Avery Allen

To find the volume of a sphere in terms of π given the formula V = (4/3)πr^3 and the diameter d = 10 cm, first, find the radius (r) using the formula r = d/2. Then, substitute the value of r into the volume formula V = (4/3)πr^3 and simplify. Here's the step-by-step process:

Given the diameter (d) = 10 cm, divide it by 2 to find the radius (r): r = d/2 r = 10 cm / 2 r = 5 cm
Substitute the radius (r = 5 cm) into the volume formula: V = (4/3)π(5 cm)^3
Calculate the volume: V = (4/3)π(125 cm^3) V = (500/3)π cm^3

Therefore, the volume of the sphere in terms of π, when the diameter is 10 cm, is (500/3)π cubic centimeters.

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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.