What is the formula to find the volume of a sphere?

What is the formula to find the volume of a sphere?

• A. V = pi x r^2 x h
• B. V = (4/3) x pi x r^3
• C. V = (1/3) x pi x r^2 x h
• D. V = 2/3 x pi x r^3

Answer: (B)

The volume of a sphere is determined by the formula V = (4/3) x π x r^3, where V represents volume, π (pi) is a constant approximately equal to 3.14159, and r symbolizes the radius of the sphere. This formula is derived from integral calculus or can also be understood geometrically by considering how the volume scales with the radius. The term r^3 emphasizes that volume grows disproportionately with an increase in radius; doubling the radius results in a volume that is eight times larger (since 2^3 = 8). Other options presented refer to different geometric shapes or volumes. For example, the first choice describes the formula for the volume of a cylinder, which includes a height (h), while the third choice outlines the formula for the volume of a cone. The fourth option is also incorrect as it does not represent any conventional solid's volume formula accurately. Using the correct formula helps calculate and understand the spatial dimensions of a sphere, making it essential for anyone studying geometry or related fields.

The volume of a sphere is determined by the formula V = (4/3) x π x r^3, where V represents volume, π (pi) is a constant approximately equal to 3.14159, and r symbolizes the radius of the sphere.

This formula is derived from integral calculus or can also be understood geometrically by considering how the volume scales with the radius. The term r^3 emphasizes that volume grows disproportionately with an increase in radius; doubling the radius results in a volume that is eight times larger (since 2^3 = 8).

Other options presented refer to different geometric shapes or volumes. For example, the first choice describes the formula for the volume of a cylinder, which includes a height (h), while the third choice outlines the formula for the volume of a cone. The fourth option is also incorrect as it does not represent any conventional solid's volume formula accurately.

Using the correct formula helps calculate and understand the spatial dimensions of a sphere, making it essential for anyone studying geometry or related fields.