Question

the volume of a spherical balloon expands as air is pumped into it. assume air is being pumped at a constant rate of 400π in³/sec.what is the radius of the balloon when its volume is 972π in³?use the formula:v=46πr3v = \frac{4}{6} \pi r ^{3} v=64​πr3

Answer 1

The radius of the given sphere will be 9/π.

What is a sphere?

• A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions.
• In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point.
• The radius of the sphere is denoted by the letter r, and the given point is its center.
• The sphere is a three-dimensional shape that is sometimes referred to as a circle's second cousin.
• A sphere is a solid shape that is round, without edges.
• Balloons, playing balls, and even light bulbs are examples of objects with sphere shapes.

So, the formula for the volume of a sphere: V = 4/3πr³

Volume is 972, then the radius will be:

• 972 = 4/3πr³
• 3(972) = 4πr³
• 2,916 = 4πr³
• πr³ = 2916/4
• πr³ = 729
• r³ = 729/π
• r = ∛729/π
• r = 9/π

Therefore, the radius of the given sphere will be 9/π.

Know more about spheres here:

brainly.com/question/22807400

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