Question

Найдите площадь поверхности и объем шара с диаметром 6 см

Answer 1

S=4πR^2;  S=4π *3^2=4*9π=36π(см^2);
V=4/3 πR^3;  V=4/3 *π*3^3=(4*3*3*3/3)π=(4*9)π=36π(см^3)

Answer 2

Calculating the Surface Area and Volume of a Sphere with a Diameter of 6 cm

To calculate the surface area and volume of a sphere with a diameter of 6 cm, we can use the following formulas:

Surface Area of a Sphere: The surface area (S) of a sphere is given by the formula: \[ S = 4 * \pi * r^2 \]

Volume of a Sphere: The volume (V) of a sphere is given by the formula: \[ V = \frac{4}{3} * \pi * r^3 \]

Where: - \( r \) is the radius of the sphere, which is half the diameter. - \( \pi \) is a mathematical constant approximately equal to 3.14.

Calculating the Surface Area and Volume

Given that the diameter of the sphere is 6 cm, the radius (r) can be calculated as half of the diameter, which is 3 cm.

Surface Area: Using the formula for the surface area of a sphere: \[ S = 4 * \pi * r^2 \] \[ S = 4 * 3.14 * 3^2 \] \[ S = 4 * 3.14 * 9 \] \[ S = 113.04 \, cm^2 \]

Volume: Using the formula for the volume of a sphere: \[ V = \frac{4}{3} * \pi * r^3 \] \[ V = \frac{4}{3} * 3.14 * 3^3 \] \[ V = \frac{4}{3} * 3.14 * 27 \] \[ V = 113.04 \, cm^3 \]

Therefore, the surface area of the sphere is 113.04 cm² and the volume of the sphere is 113.04 cm³.