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Problem 72

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Problem 68

A sporting goods manufacturer designs a golf ball having a : volume of 2.48 cubic inches.

(a) What is the radius of the golf ball?

(b) The volume of the golf ball varies between 2.45 cubic inches. How does the radius vary?

(c) Use the $\varepsilon-\delta$ definition of limit to describe this situation. Identify $\varepsilon$ and $\delta .$

Answer

$\epsilon=\frac{0.843-0.836}{2}=0.0035$

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## Discussion

## Video Transcript

Okay, Part A, we know sees two pi times the radius so plugging in. This gives us articles 1.2 sevens. The volume of the test ball is 4/3 pi times. The radius cubed equals 8.58 inches and coats volume. It's obviously cute. Okay, moving on into park be We know the amount of space taken up by the test ball is equivalent to the volume of a cylinder, which is subtracting the volume of three tennis balls. So we have pi times the radius 1.43 squared times the height minus three times the volume of the tennis ball, which we figured out in the previous slide. This gives us for 51.4 months, 25.7, which gives us 25.66 inches cute.

## Recommended Questions

Three tennis balls are stored in a cylindrical container with a height of 8 inches and a radius of 1.43 inches. The circumference of a tennis ball is 8 inches.

a. Find the volume of a tennis ball.

b. Find the amount of space within the cylinder not taken up by the tennis balls.

The volume of a sphere is found with the formula $V=\frac{4}{3} \pi r^{3},$ where $r$ is the length of the radius of the sphere.

A ball in the shape of a sphere has a volume of $288 \pi$ in.3. What is the radius of the ball?

(FIGURE CANNOT COPY)

The diameter of a sphere is measured to be 5.36 in. Find (a) the radius of the sphere in centimeters, (b) the surface area of the sphere in square centimeters, and (c) the volume of the sphere in cubic centimeters.

A spherical steel ball bearing has a diameter of 2.540 $\mathrm{cm}$ at $25.00^{\circ} \mathrm{C}$ (a) What is its diameter when its temperature is raised to $100.0^{\circ} \mathrm{C}$ ? (b) What temperature change is required to increase its volume by 1.000$\%$ ?

A spherical steel ball bearing has a diameter of 2.540 $\mathrm{cm}$ at $25.00^{\circ} \mathrm{C}$ . (a) What is its diameter when its temperature is raised to $100.0^{\circ} \mathrm{C}$ ? (b) What temperature change is required to increase its volume by 1.000$\%$ ?

The surface area of a sphere is given by $A(r)=4 \pi r^{2},$ where $r$ is in inches and $A(r)$ is in square inches. The function $C(x)=6.4516 x$ takes $x$ square inches as input and outputs the equivalent result in square centimeters. Find $(C \circ A)(r)$ and explain what it represents.

Multiple Choice The circumference of a basketball for college women must be from 28.5 in. to 29.0 in. Which absolute value inequality best represents the circumference of the ball?

(A) $|C-0.25| \geq 28.5$

(B) $|C-0.25| \leq 29.0$

(C) $|C-28.75| \leq 0.25$

(D) $|C-28.75| \geq 0.25$

A solid metal ball with radius 8 $\mathrm{cm}$ is melted down and recast as a solid cone with the same radius.

a. What is the height of the cone?

b. Use a calculator to show that the lateral area of the cone is about 356 more than the area of the sphere.

A sphere is inscribed in a cube with a volume of 64 cubic inches. What is the surface area of the sphere? Explain your reasoning.

STANDARDIZED TEST PRACTICE An NCAA (National Collegiate Athletic Association) basketball has a radius of $4 \frac{3}{4}$ inches. What is its surface area?

$A \frac{361 \pi}{16} \mathrm{in}^{2}$

$B \frac{361 \pi}{4} \mathrm{in}^{2}$

C $19 \pi$ in $^{2}$

D $361 \pi$ in $^{2}$