A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
This prism has a volume of 240 cm3.
What would the volume of the prism be if each dimension was halved? (Scale factor is
http://static.k12.com/bank_packages/files/media/mathml_68f74329bc2e147090cb3e6f27fbce4255c06f3b_1.gif
.)
A.
120 cm3
B.
480 cm3
C.
30 cm3
D.
60 cm3
anonymous
 one year ago
This prism has a volume of 240 cm3. What would the volume of the prism be if each dimension was halved? (Scale factor is http://static.k12.com/bank_packages/files/media/mathml_68f74329bc2e147090cb3e6f27fbce4255c06f3b_1.gif .) A. 120 cm3 B. 480 cm3 C. 30 cm3 D. 60 cm3

This Question is Closed

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2When you change the side of a solid by a scale factor of k, the volume changes by a factor of \(k^3\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Your scale factor is 1/2 What is \((1/2)^3\) ?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2We need to find this: \((\dfrac{1}{2}) ^3\) Have you learned exponents?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2For example, what is \(3^2\) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[1\frac{ 1 }{ 2 }\]

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2No, this is how exponents work. \(3^2 = 3 \times 3 = 9\) For example, \(4^3 = 4 \times 4 \times 4 = 64\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2The base tells you which number is going to be multiplied. The exponent tells you how many of the bases to use. \(3^2\) The base is 3, so 3 will be multiplied. The exponent is 2, so there will be two bases multiplied, or two 3's multiplied. That means \(3^2 = 3 \times 3\) and \(3 \times 3 = 9\) so \(3^2 = 3 \times 3 = 9\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Let's use a higher exponent. What is 2^4? You need to multiply four 2's together. \(2^4 = 2 \times 2 \times 2 \times 2 = 16\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Do you have a better understanding of exponents now?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Ok. In your problem, the side was changes by a scale factor of 1/2 The rule is if the sides changes by a factor of k, the volume changes by a factor of k^3. In your case, that means the volume changes by a factor of \(\left( \dfrac{1}{2} \right)^3\) Now we need to use our knowledge of exponents and find what \(\left( \dfrac{1}{2} \right)^3\) is equal to.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[1\frac{ 1 }{ 2 }\]

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2According to what the exponents mean, \(\left( \dfrac{1}{2} \right)^3 = \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[1\frac{ 1 }{ 2 }\]

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2\(1 \dfrac{1}{2} = \dfrac{1}{2} + \dfrac{1}{2} +\dfrac{1}{2} \) We are not adding the fractions. We are multiplying them together.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2\(\left( \dfrac{1}{2} \right)^3 = \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{2 \times 2 \times 2} = \dfrac{1}{8}\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.21/8 is quite different from 1 1/2

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Ok. Now we know that the volume factor is 1/8 when the side factor is 1/2. That means that when the side of a solid becomes half what it used to be, the volume becomes 1/8 of what it used to be.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2If your prism started with a volume of 240 cm^3, and each dimension became half, that means the volume is only 1/8 of 240 cm^3. What is 240 cm^3 divided by 8 ?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Here is an explanation with a figure that sometimes makes things easier to understand.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2dw:1435895261732:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Yes, the answer is 30 cm^3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank u i have like 3 more can u help me with them

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2In the figure above the cube has a side of 4 cm. The volume of the cube is \(V = s^3 = (4 ~cm)^3 = 4 ~cm \times 4 ~cm \times 4 ~cm = 64 ~cm^3\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Now let's draw a smaller cube in which every side is half of the original one. dw:1435895446522:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2The volume of the new cube is: \(V = s^3 = (2 ~cm)^3 = 2 ~cm \times 2 ~cm \times 2 ~cm = 8 ~cm^3\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Since the new cube has a side that is half of the original cube (2 cm is half of 4 cm), the scale factor of the sides is 1/2. That means the scale factors of the volumes is (1/2)^3 = 1/8 Now look at the volumes: 64 cm^3 and 8 cm^3 Sure enough, 8 cm^3 is 1/8 the volume of the original cube, 64 cm^3.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.