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A rectangular box has length 9 feet, width 4 feet, and height 6 feet. Find its volume and surface area.

  1. 216 cu. ft
  2. 228 sq. ft

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A rectangular suitcase has length 22 inches, width 14 inches, and height 9 inches. Find its volume and surface area.

  1. 2,772 cu. in.
  2. 1,264 sq. in.

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Volume and surface area of a cube

A cube    is a rectangular solid whose length, width, and height are equal. See Volume and Surface Area of a Cube, below. Substituting, s for the length, width and height into the formulas for volume and surface area of a rectangular solid, we get:

V = L W H S = 2 L H + 2 L W + 2 W H V = s · s · s S = 2 s · s + 2 s · s + 2 s · s V = s 3 S = 2 s 2 + 2 s 2 + 2 s 2 S = 6 s 2

So for a cube, the formulas for volume and surface area are V = s 3 and S = 6 s 2 .

Volume and surface area of a cube

For any cube with sides of length s ,

An image of a cube is shown. Each side is labeled s. Beside this is Volume: V equals s cubed. Below that is Surface Area: S equals 6 times s squared.

A cube is 2.5 inches on each side. Find its volume and surface area.

Solution

Step 1 is the same for both and , so we will show it just once.

Step 1. Read the problem. Draw the figure and
label it with the given information.
.
Step 2. Identify what you are looking for. the volume of the cube
Step 3. Name. Choose a variable to represent it. let V = volume
Step 4. Translate.
Write the appropriate formula.

V = s 3
Step 5. Solve. Substitute and solve. V = ( 2.5 ) 3
V = 15.625
Step 6. Check: Check your work.
Step 7. Answer the question. The volume is 15.625 cubic inches.
Step 2. Identify what you are looking for. the surface area of the cube
Step 3. Name. Choose a variable to represent it. let S = surface area
Step 4. Translate.
Write the appropriate formula.

S = 6 s 2
Step 5. Solve. Substitute and solve. S = 6 ( 2.5 ) 2
S = 37.5
Step 6. Check: The check is left to you.
Step 7. Answer the question. The surface area is 37.5 square inches.
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For a cube with side 4.5 meters, find the volume and surface area of the cube.

  1. 91.125 cu. m
  2. 121.5 sq. m

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For a cube with side 7.3 yards, find the volume and surface area of the cube.

  1. 389.017 cu. yd.
  2. 319.74 sq. yd.

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A notepad cube measures 2 inches on each side. Find its volume and surface area.

Solution

Step 1. Read the problem. Draw the figure and
label it with the given information.
.
Step 2. Identify what you are looking for. the volume of the cube
Step 3. Name. Choose a variable to represent it. let V = volume
Step 4. Translate.
Write the appropriate formula.

V = s 3
Step 5. Solve the equation. V = 2 3
V = 8
Step 6. Check: Check that you did the calculations
correctly.
Step 7. Answer the question. The volume is 8 cubic inches.
Step 2. Identify what you are looking for. the surface area of the cube
Step 3. Name. Choose a variable to represent it. let S = surface area
Step 4. Translate.
Write the appropriate formula.

S = 6 s 2
Step 5. Solve the equation. S = 6 2 2
S = 24
Step 6. Check: The check is left to you.
Step 7. Answer the question. The surface area is 24 square inches.
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A packing box is a cube measuring 4 feet on each side. Find its volume and surface area.

  1. 64 cu. ft
  2. 96 sq. ft

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A wall is made up of cube-shaped bricks. Each cube is 16 inches on each side. Find the volume and surface area of each cube.

  1. 4,096 cu. in.
  2. 1536 sq. in.

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Find the volume and surface area of spheres

A sphere is the shape of a basketball, like a three-dimensional circle. Just like a circle, the size of a sphere is determined by its radius, which is the distance from the center of the sphere to any point on its surface. The formulas for the volume and surface area of a sphere are given below.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
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
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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