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"#

#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"#
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Answer 2

a. To find the volumes of the baseball and softball, we use the formula for the volume of a sphere:

[ V = \frac{4}{3}\pi r^3 ]

Given that the great circle circumference is equal to the circumference of the sphere ((2\pi r)), we can find the radius ((r)) of each ball using the formula:

[ 2\pi r = \text{circumference} ]

From this, we can solve for (r). Once we have the radius, we can plug it into the formula for the volume of a sphere to find the volumes of the baseball and softball.

b. To find the surface areas of the baseball and softball, we use the formula for the surface area of a sphere:

[ A = 4\pi r^2 ]

We already have the radius ((r)) of each ball from part (a). Plugging it into the formula will give us the surface areas of the baseball and softball.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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