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How many cubic inches of candy will fit in a cone-shaped piñata that is 18 inches long and 12 inches across its base? Round the answer to the nearest hundredth.

678.24 cu. in.

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What is the volume of a cone-shaped party hat that is 10 inches tall and 7 inches across at the base? Round the answer to the nearest hundredth.

128.2 cu. in.

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Summary of geometry formulas

The following charts summarize all of the formulas covered in this chapter.

A table is shown that summarizes all of the formulas in the chapter. The first cell is for Supplementary and Complementary Angles, and says that the measure of angle A plus the measure of angle B equals 180 degrees for supplementary angles A and B and the measure of angle C plus the measure of angle D equals 90 degrees for complementary angles C and D. There is an image of two angles A and B that together form a straight line and two angles C and D that together form a right angle. The next cell says Rectangular Solid and shows the formulas Volume equals LWH and Surface Area equals 2LH plus 2LW plus 2WH. An image of a rectangular solid with sides L, W, and H is shown. The next cell says Triangle. An image of a triangle is shown with sides a, b, and c, vertices A, B, and C, and height h. It says, “For triangle ABC, angle measures measure of angle A plus measure of angle B plus measure of angle C equal 180 degrees. Below this is Perimeter, P equals a plus b plus c. Below this is Area, A equals one-half bh. The next cell says Cube and shows an image of a cube with sides s. It says Volume V equals s cubed and Surface Area S equals 6 times s squared. The next cell says Similar Triangles. It shows two similar triangles ABC and XYZ. It says if triangle ABC is similar to triangle XYZ, then measure of angle A equals measure of angle X, measure of angle B equals measure of angle Y, and measure of angle C equals measure of angle Z. It then says a over x equals b over y equal c over z. The next cell says Sphere and shows an image of a sphere with radius r. It says volume V equals four-thirds times pi times r and Surface Area S equals 4 times pi times r squared. The next cell says Circle. There is an image with two radii labeled r and the diameter labeled d. It says Circumference C equals 2 pi times r and C equals pi times d. It says Area equals pi times r squared. The next cell says Cylinder and shows an image of a cylinder with height h and radius of the base r. It says Volume V equals pi times r squared times h. Below this is V equals Bh. Below that is Surface Area S equals 2 times pi times r squared plus 2 times pi times rh. The next cell says Rectangle and shows an image of a rectangle with sides W and L. It says Perimeter P equals 2L plus 2W, then Area A equals LW. The next cell says Cone and shows an image of a cone with height h and radius of the base r. It says Volume V equals one-third times pi times r squared times h. The last cell says Trapezoid and shows an image of a trapezoid with bases little b and capital B, and height h. It says Area A equals one-half times h times parentheses little b plus capital B. This image shows a row with three columns. The first column says Rectangular solid with the formula below that says volume: V equals LWH. Under this, it says Surface Area: S equals 2LH plus 2LW plus 2WH. An image shows an image of a rectangular solid with the sides labeled L , W and H. The middle column says Rectangle. Under this it says Perimeter P equals 2L plus 2W, then Area A equals LW.  An image of a rectangle with sides W and L. The right column says Cube. Under this it says “Volume: V equals s to the third power.” Under this is says “Surface area: S equals 6 times s squared. Below it is an image of a cube with three sides labeled “s”.

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Key concepts

  • Volume and Surface Area of a Rectangular Solid
    • V = L W H
    • S = 2 L H + 2 L W + 2 W H
  • Volume and Surface Area of a Cube
    • V = s 3
    • S = 6 s 2
  • Volume and Surface Area of a Sphere
    • V = 4 3 π r 3
    • S = 4 π r 2
  • Volume and Surface Area of a Cylinder
    • V = π r 2 h
    • S = 2 π r 2 + 2 π r h
  • Volume of a Cone
    • For a cone with radius r and height h :
      Volume: V = 1 3 π r 2 h

Practice makes perfect

Find Volume and Surface Area of Rectangular Solids

In the following exercises, find the volume and the surface area of the rectangular solid with the given dimensions.

length 2 meters, width 1.5 meters, height 3 meters

  1. 9 cu. m
  2. 27 sq. m

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length 5 feet, width 8 feet, height 2.5 feet

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length 3.5 yards, width 2.1 yards, height 2.4 yards

  1. 17.64 cu. yd.
  2. 41.58 sq. yd.

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length 8.8 centimeters, width 6.5 centimeters, height 4.2 centimeters

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In the following exercises, solve.

Moving van A rectangular moving van has length 16 feet, width 8 feet, and height 8 feet. Find its volume and surface area.

  1. 1,024 cu. ft
  2. 640 sq. ft

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Gift box A rectangular gift box has length 26 inches, width 16 inches, and height 4 inches. Find its volume and surface area.

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Carton A rectangular carton has length 21.3 cm, width 24.2 cm, and height 6.5 cm. Find its volume and surface area.

  1. 3,350.49 cu. cm
  2. 1,622.42 sq. cm

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Shipping container A rectangular shipping container has length 22.8 feet, width 8.5 feet, and height 8.2 feet. Find its volume and surface area.

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In the following exercises, find the volume and the surface area of the cube with the given side length.

5 centimeters

  1. 125 cu. cm
  2. 150 sq. cm

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10.4 feet

  1. 1124.864 cu. ft.
  2. 648.96 sq. ft

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In the following exercises, solve.

Science center Each side of the cube at the Discovery Science Center in Santa Ana is 64 feet long. Find its volume and surface area.

  1. 262,144 cu. ft
  2. 24,576 sq. ft

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Museum A cube-shaped museum has sides 45 meters long. Find its volume and surface area.

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Base of statue The base of a statue is a cube with sides 2.8 meters long. Find its volume and surface area.

  1. 21.952 cu. m
  2. 47.04 sq. m

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Tissue box A box of tissues is a cube with sides 4.5 inches long. Find its volume and surface area.

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Find the Volume and Surface Area of Spheres In the following exercises, find the volume and the surface area of the sphere with the given radius. Round answers to the nearest hundredth.

3 centimeters

  1. 113.04 cu. cm
  2. 113.04 sq. cm

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7.5 feet

  1. 1,766.25 cu. ft
  2. 706.5 sq. ft

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In the following exercises, solve. Round answers to the nearest hundredth.

Exercise ball An exercise ball has a radius of 15 inches. Find its volume and surface area.

  1. 14,130 cu. in.
  2. 2,826 sq. in.

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Balloon ride The Great Park Balloon is a big orange sphere with a radius of 36 feet . Find its volume and surface area.

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Questions & Answers

price elasticity of demand is the degree of responsiveness of a quantity demanded to the change in price of the commodity in question.
Gladys Reply
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Thelma Reply
it helps to make the correct choice
Gladys
it helps firm to produce products that will bring more profit
Gladys
the difference between needs and wants
londiwe Reply
needs are things that we basically can't live without wants are just luxury things
Thelma
needs are things without them we can't live but want are things without we can live
KP
what is education
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it's a process in which we give or receiving methodical instructions
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When you make a Scedule of the demand you made
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What is macroeconomics
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It's one of the two branches of Economics that deal with the aggregate economy.
Mayen
it's about inflation, occupation, gdp and so on
alberto
What is differences between Microeconomics and Macroeconomic?
Bethrand
microeconomics focuses on the action of individual agents in the economy such as businesses, workers and household. while macroeconomics looks at the economy as a whole. it focuses on broad issues in the economy such as government deficit, economy growth, levels of exports and imports, and
Thelma
inflationary increase in prices
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a price floor of 24 imposed
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Fixed Costs per week Variable Costs per bear Rent & Rates of Factory Hire & machines Heating & Lighting Repayment of Bank Loan K100.00 K45.00 K5.00 K50.00 Materials Foam Wages K6.00 K1.00 K1.00 Total K200.00 K8.00
Richard
one of the scarce resources that constrain our behaviour is time. each of us has only 24 hours in a day. how do you go about allocating your time in a given day among completing alternatives? once you choose a most important use of time. why do you not spend all your time to it. use the notion of op
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mani Baba. First learn the spelling of Economics
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Economics- The study of how people use their limited resources to tey and satisfy unlimited wants.
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Difference between extinct and extici spicies
Amanpreet Reply
in a comparison of the stages of meiosis to the stage of mitosis, which stages are unique to meiosis and which stages have the same event in botg meiosis and mitosis
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Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.
Mapo Reply
The formulation of new memories is sometimes called ________, and the process of bringing up old memories is called ________.
Mapo Reply
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
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how do you translate this in Algebraic Expressions
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why surface tension is zero at critical temperature
Shanjida
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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Practice Key Terms 3

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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