Question

A regulation baseball (hardball) has a great circle circumference of 9 inches; a regulation softball has a great circle circumference of 12 inches. a. Find the volumes of the two types of balls. b. Find the surface areas of the two types of balls?

Answer 1

`color(blue)("Volume of baseball " V_h = 12.31 " cub inch"`

`color(blue)("Volume of softball " V_2 = 29.18 " cub inch"`

`color(green)("Surface Area of baseball " A_h = 25.78 " sq inch"`

`color(green)("Surface Area of softball " A_s = 45.84 " sq inch"`

Explanation:

`color(crimson)("Volume of Sphere " V = (4/3) pi r^3`

`color(crimson)("Surface Area of Sphere " A_s = 4 pi r^2`

`color(crimson)("Circumference of circle " C = 2 pi r`

`color(crimson)("Area of circle "A_c = pi r^2`

`"Given : " C_h = 2 pi r_h = 2pi * 9 " inch"`

`:. r_h = 9 / 2pi`

`V_h = (4/3) pi (r_h)^3 = (4/3) * pi * (9/(2pi))^3`

`V_h = 12.31 " cub inch"`

`A_h = 4 pi( r_h)^2 = 4* pi * (9/(2pi))^2 = 25.78 " sq inch"`

`"Given : " C_s = 2 pi r_h = 2pi * 12 " inch"`

`:. r_s = 12 / 2pi`

`V_s = (4/3) pi (r_s)^3 = (4/3) * pi * (12/(2pi))^3`

`V_s = 29.18 " cub inch"`

`A_s = 4 pi( r_s)^2 = 4* pi * (12/(2pi))^2 = 45.84 " sq inch"`