College

Tennis balls with a diameter of 2.6 inches are sold in cans of three.

The can is a cylinder. What is the volume of the space NOT occupied

by the tennis balls? (Assume the tennis balls touch the can on all

sides, top and bottom.) Round to the nearest tenth and show all steps

and reasoning.

How can you tell if a formula represents Length, an Area, or Volume? What do you look for in

the formula?

Explain how you could get a formula for the volume of the

16 cm

solid.

Find the diagonal of the box, AD, using the Pythagorean

Theorem twice - 1. To find BD and 2. To find AD.

AB = 12 in

BC= 18 in

CD = 4 in

Show all steps for findin the diagonal of the box above using the formula instead of the

Pythagorean Theorem twice.

0

9

Diagonal of a box of

dimensions a, b, c

a2 + b2+c2 = d2

Tennis balls with a diameter of 2 6 inches are sold in cans of three The can is a cylinder What is the volume of

Answer :

The volume of the solid is combined of a cone, cylinder, and hemisphere is

329.7 cubic cm.

What are the formulas for the volume of a cone, cylinder, and half of a sphere?

The volume of a cone is (1/3)πr²h.

The volume of a cylinder is πr²h.

The volume of half a sphere or a hemisphere is (1/3)πr³.

The given figure has a volume combined of a cone, cylinder, and hemisphere.

∴ The volume of the solid is = (1/3)π(3)²×5 + π(3)²×(8) + (2/3)π(3)³ cubic cm.

= (47.1 + 226.08 + 56.52) cubic cm.

= 329.7 cubic cm.

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Final answer:

To determine the volume of the can not occupied by tennis balls, subtract the volume of the three balls from the volume of the can. The volumes are calculated using the respective formulas for cylinders and spheres. Typically, length is represented by a single measure, an area is represented by square measure, and volume by cubic measure.

Explanation:

The volume of space not occupied by the tennis balls can be determined by finding the difference between the volume of the can and the combined volume of the three tennis balls. The volume of the cylinder (the can) is found by using the formula V = πr^2h, where r is the radius, and h is the height. The volume of a sphere (the tennis ball) is determined by (4/3)πr^3. Assume the height of the can is just enough for three tennis balls, so it would be 7.8 inches (3 times diameter of the tennis ball, which is 2.6 inches). Therefore, calculate the volumes of the can and balls, then subtract the combined tennis balls' volume from the cylinder's volume. To check if a formula represents a length, area, or volume, typically a length will be a singular measure (i.e., meters, inches), area is a square measure (i.e., square meters, square inches), and volume is a cubic measure (square meters, cubic inches).

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