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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

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
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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