Question

The radius of a sphere is 6 units. Which expression represents the volume of the sphere, in cubic units?
π(6)2
π(6)3
π(12)2
π(12)3

Answer 1

By definition, the volume of a sphere is given by:

$V = (\frac{4}{3}) * (\pi) * (r ^ 3)$

Where,

r: sphere radio

Substituting values we have:

$V = (\frac{4}{3}) * (\pi) * (6 ^ 3)$

Note: all the expressions given, they need the factor 4/3

Answer:

An expression that represents the volume of the sphere, in cubic units is:

$V = (\frac{4}{3}) * (\pi) * (6 ^ 3)$

option 2

Answer 2

The volume of the sphere with a radius of 6 units can be written as $2\pi(12)^2\ \ \rm or\ \ \dfrac{4}{3}\pi6^3$.

What is the volume of the sphere?

The volume of the sphere with a radius of r is given by the formula,

$\text{Volume of the Sphere} = \dfrac{4}{3}\pi r^3$

Given to us

The radius of the sphere, R = 6 units

We know the formula of the volume of a sphere, therefore, the volume of the sphere can be given as,

$\text{Volume of the Sphere} = \dfrac{4}{3}\pi r^3$

Substitute the value of the radius,

$\text{Volume of the Sphere} = \dfrac{4}{3}\pi (6)^3$

                                  $=\dfrac{4}{3}\pi (6 \times 6 \times 6)\\\\=288 \pi\\\\= 2 \pi(12)^2 \rm\ unit^3$

Hence, the volume of the sphere with a radius of 6 units can be written as $2\pi(12)^2\ \ \rm or\ \ \dfrac{4}{3}\pi6^3$.

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