Early golf balls were smooth spheres. Later it was discovered that golf balls flew better when they were dimpled. On January 1 , 1932, the United States Golf Association set standards for the weight and size of a golf ball. The minimum diameter of a regulation golf ball is $1.680$ inches. Use $3.14$ for $\pi$. Round to the nearest hundredth.

Find the volume of a smooth golf ball with the minimum diameter allowed by the United States Golf Association.

An oil funnel is in the shape of a cone. It has a diameter of 4 inches and a height of 6 inches. If the end of the funnel is plugged, how much oil can the funnel hold before it overflows?

The Sun Pyramid in Teotihuacan, Mexico, is larger than the Feathered Serpent Pyramid. The sides of the square base and the height are each about 3.3 times larger than the Feathered Serpent Pyramid. How many times larger is the volume of the Sun Pyramid than the Feathered Serpent Pyramid?

The United States Golf Association (USGA) sets performance standards for golf balls. For example, the initial velocity of the ball may not exceed 250 feet per second when measured by an apparatus approved by the USGA. Suppose a manufacturer introduces a new kind of ball and provides a sample for testing. Based on the mean speed in the test, the USGA comes up with a P-value of 0.34. Explain in this context what the “34%” represents.

USGA golf ball tests. The United States Golf Association (USGA) tests all new brands of golf balls to ensure that they meet USGA specifications. One test conducted is intended to measure the average distance traveled when the ball is hit by a machine called "Iron Byron," a name inspired by the swing of the famous golfer Byron Nelson. Suppose the USGA wishes to estimate the mean distance for a new brand to within 1 yard with $90 \%$ confidence. Assume that past tests have indicated that the standard deviation of the distances Iron Byron hits golf balls is approximately 10 yards. How many golf balls should be hit by Iron Byron to achieve the desired accuracy in estimating the mean?

Is the sample mean always the most frequently occurring value? If so, explain why. If not, give an example.

The United States Golf Association (USGA) tests all new brands of golf balls to ensure that they meet USGA specifications. One test conducted is intended to measure the average distance traveled when the ball is hit by a machine called "lron Byron." Suppose the USGA wishes to estimate the mean distance for a new brand to within 1 yard with 90% confidence. Assume that past tests have indicated that the standard deviation of the distances Iron Byron hits golf balls is approximately 10 yards. How man y golf balls should be hit by Iron Byron to achieve the desired accuracy in estimating the mean?

Will exactly half of the observations in a sample always fall below the mean? Provide an example to illustrate your answer.

Eight measurements were made on the inside diameter of forged piston rings used in an automobile engine. The data (in millimeters) are 74.00, 74.003, 74.015, 74.000, 74.005, 74.002, 74.005, and 74.004. Calculate the sample mean and sample standard deviation, construct a dot diagram, and comment on the data.

A hemisphere is half of a sphere. Explain how you would find the volume of a hemisphere.

A frying pan has a diameter of 11 inches. What is the area to the nearest square inch of the smallest cover that will fit on top of the pan?

What is the relationship between the volume of a cylinder and a cone with the same height and same radius?

What is the area of a circle whose radius is 3 cm?

A hemisphere is half of a sphere. Explain how you would find the volume of a hemisphere.