Show:
Volume of Cones
Volume of Spheres
Volume of Cylinders
Volume of Composite Figures
Mixed Review
100
V = 1/3πr²h
What is the volume formula for a cone?
100
V = 4/3r³
What is the volume formula of a sphere?
100
V = πr²h
What is the volume formula for a cylinder?
100
It depends on which shapes are involved.
What is how to find the volume of composite figures.
100
Only the Volume formula for Sphere
Which one of the volume formulas involves cubing the radius instead of squaring the radius?
200
The formula for finding the volume of a cone is V = 1 3 πr2h. The radius of a cone is 5 cm and the height of a cone is 10 cm. What is the approximate volume of the cone? A) 2,356 cm3 B) 52 cm3 C) 262 cm3 D) 524 cm3
C: 262 cm³
200

a Sphere has a volume of 904.8 cubic meters.  what is the radius of the sphere?

what is 6 meters

200
Find the volume of a cylinder with a radius of 3 cm and a height of 7 cm. A) 9π cm3 B) 21π cm3 C) 42π cm3 D) 63π cm3
D: 63π cm³
200

You have a cylinder with a height of 10 in and a radius with 8 inches that has a cone on top of it with a height of 15 inches. What is the total volume?

3015.93 cubic inches

200
A rabbit has found some carrots and wants to hide them in her cylindrical rabbit hole. If the carrots have the same base (at their thick end) diameter as the hole does and are also the same height as the rabbit hole, how many carrots will fit in the hole? [V = πr2h] A) 2 carrots. B) 3 carrots. C) 9.4 carrots. D) π carrots.
B: 3 The question is asking about how many cones can fit in a cylinder of equal height and diameter. Since the formula for the volume of a cylinder is πr2 h and the formula for the volume of a cone is 1 3 (πr2)· h, the hole is 3 times the volume of a carrot and 3 carrots will fill the hole. The rabbit needs a larger home.
300
What is the volume of this cone? A) 41.9 ft3 B) 125.6 ft3 C) 240 ft3 D) 501.4 ft3
A: 41.9 ft³ The volume of a cone is the area of its circular base · its altitude, divided by 3, or 1 3 πr2 h. Here, this is equal to 1 3 40π, or 41.9 ft3
300
Leah has two congruent beach balls. The diameter of one ball is 20 inches. Which choice is the closest for the volume of the second ball? A) 3721 in3 B) 4187 in3 C) 11164 in3 D) 33493 in3
B: 4187 in³
300
Sally wants to fill ten 8-inch tea glasses. How much tea does she need? A) 80 ounces B) 40 ounces C) 80 cubic inches D) Not enough information to answer
D
300
A tin man has a head that is a cylinder with a cone on top. The height of the cylinder is 12 inches and the height of the cone is 6 inches. The radius of both the cylinder and the cone is 4 inches. What is the volume of the tin man's head in terms of pi? A) 192π in3 B) 224π in3 C) 384π in3 D) 912π in3
B: 224π in³ The volume of a cylinder is πr2 h and the volume of a cone is 1 3 πr2 h. When we plug in the dimensions, we get π(42 )(12) + 1 3 π(42 )(6) = 224π in3.
300
Assume Cylinder A and Cone B are the same height and the bases have the same radius. If A has a volume of 18π cm3, what is the volume of B? A) 6π cm3 B) 18π cm3 C) 24π cm3 D) 36π cm3
A: 6π cm³ Vcylinder = Bh = 18π cm3 Vcone = 1 3 Bh = 1 3 18π cm3 = 6π cm3
400
An ice cream cone is filled with vanilla and chocolate ice cream at a ratio of 2:3. If the diameter of the cone is 2 inches and the height is 5 inches, approximately what is the volume of chocolate ice cream in the cone? (round to nearest tenth) A) 1.6 in3 B) 2.1 in3 C) 3.1 in3 D) 5.2 in3
C. 3.1 in³ 3.1 in3 of chocolate ice cream. V = 1 3 πr2 h V = 1 3 π(12)(5) = 5.236 in3 Chocolate equals 3 5 of the ice cream. then, 3 5 x 5.236 = 3.142 ≈ 3.1 in3
400
If the volume of a spherical ball is 113.04 cubic inches, what is the radius? A) 3 inches B) 9 inches C) 18 inches D) 27 inches
A: 3 inches
400
Jeffrey is buying mulch for a circular flower garden with a diameter of 12 feet. The layer of mulch needs to be 4 inches thick. What is the volume of mulch needed for the flower garden? A) 37.7 ft3 B) 113.1 ft3 C) 452.4 ft3 D) 651.4 ft3
A: 37.7 ft³
400
Find the volume of a figure of a cylinder with a hemisphere on top if the radius of the hemisphere and cylinder is 6 inches and the height of the cylinder is 12 inches. Find the volume in terms of pi. A) 117π in3 B) 576π in3 C) 720π in3 D) 1008π in3
B: 576π in³ The formula for the volume of a cylinder is πr2 h and the volume of a hemisphere is 1 2 · 4 3 πr3 or 2 3 πr3. When we plug in 6 for r and 12 for h, we get π(62)(12) + 2 3 π(63) which is 576π in3.
400
Ray is late for work, but would like to drink some coffee before he leaves. The coffee in the pot is too hot, so Ray puts 20 small ice cubes in a mug before pouring in the coffee. The ice cubes measure 1 cm per side. The mug is cylindrical, and has a height of 9 cm and a base of 7 cm. What is volume of the coffee that will fill the mug after the ice cubes have been added (round to the nearest whole number)? A) 113 cm3. B) 326 cm3. C) 346 cm3. D) 424 cm3.
B: The volume of the mug is the area of its base · the mug's height, or πr2 h. This is 3.5 cm · 3.5 cm. · 9 · π, or 346.2 cm3. The volume of each ice cube is 1 cubic centimeter, so 20 of them will occupy 20 cm3. This leaves 326 cm3 for the coffee.
500
An ice cream cone is filled with vanilla and chocolate ice cream at a ratio of 2:1. If the diameter of the cone is 2 inches and the height is 6 inches, approximately what is the volume of vanilla ice cream in the cone? (round to nearest tenth) A) 1.0 in3 B) 2.1 in3 C) 4.2 in3 D) 6.3 in3
C..4.2 in³ 4.2 in3 of vanilla ice cream. V = 1 3 πr2 h V = 1 3 π(12)(6) = 6.283 in3 Vanilla is 2 3 of the ice cream. then, 2 3 x 6.283 = 4.189 ≈ 4.2 in3
500
There is 1.4 ounces of juice in 7 in3 of tangerines. If you have a sack of tangerines which each have a diameter of 2 inches, approximately how many tangerines do you need to make a 7 ounce glass of juice? (round to nearest whole number) A) 2 B) 4 C) 6 D) 8
D. 8: 8 tangerines. V = 4 3 πr3 V = 4 3 π13 = 4.189 in3 Then, x 4.189 = 1.4 7 x = 0.8378 ounces in one tangerine. Thus, 7.0 0.8378 = 8.355 whole tangerines.
500
The portion of a student’s ballpoint pen that contains the ink is a cylinder with a diameter of 0.400 cm and a height of 11.5 cm. If the ink lasts 7 weeks, what is the volume of ink that the student uses each week? A) 0.21 cm3. B) 0.92 cm3. C) 1.84 cm3. D) 12.9 cm3.
A: 0.21 cm³
500
If the circumference of the circular base of a cylinder is doubled, how does the volume of the cylinder change? A) The volume doubled. B) The volume tripled. C) The volume quadrupled. D) The volume is eight times larger.
C. The volume quadrupled. If the circumference of the circular base of a cylinder is doubled, The volume quadrupled. C = 2πr, V = πr2h If the circumference is doubled, then the radius is doubled. In the volume formula, when you square the doubled radius, you end up with four times the original volume.
500
An unopened can of iced tea contains 350 cubic centimeters of liquid. If the can is 5 inches long and has a 0.8-inch diameter, which is the BEST estimate of the volume of iced tea contained in the top 3 inches of the can? A) 106 cubic centimeters. B) 140 cubic centimeters. C) 210 cubic centimeters. D) 382 cubic centimeters.
C: 210 cubic centimeters. A can of iced tea is the approximate shape of a cylinder. Each inch of can’s 5-inch length contains the same volume. Set up a proportion volume height = volume height or 350 5 = x 3 and solve for x. x = 210 cubic centimeters. The diameter of the can is irrelevant here.