area grows by the scale factor squared
volume grows as the cube.
So, since the scale factor is 2/3, the new values are:
area = 18 * (2/3)^2 = 72/9 = 8
volume = 6 * (2/3)^3 = 48/27 = 16/9 = 1.777...
so that people know i am not looking for someone to just tell me the answer but can you please help me.
The surface area of a solid is 18 in.2, and its volume is 6 in.3. The ratio of corresponding dimensions of a similar solid is 2 over 3. Find the surface area and volume of the similar solid.
S.A. = 12 in.2; V = 4 in.3
S.A. = 8 in.2; V = 2.6 repeating in.3
S.A. = 8 in.2; V = 1.7 repeating in.3
S.A. = in.2; V = 1.7 repeating in.3
4 answers
oobleck
i dont get the (2/3)^2 and (2/3)^3 how do you find out that (2/3)^2 =72/9 and (2/3)^3 =48/27 i haven't been in school at all this year so i dont get anything from this school year
i dont get the (2/3)^2 and (2/3)^3 how do you find out that (2/3)^2 =72/9 and (2/3)^3 =48/27 i haven't been in school at all this year so i dont get anything from this school year
area is length * width, so if both are scaled by a factor of 2/3,
(2/3 length)(2/3 width) = (2/3)(2/3)(length*width) = (2/3)^2 * old area
same for volume, using 3 dimensions.
If you carry the units (in) with the values, this becomes clear.
If the old area is 18 in^2, that might be 6in * 3in
Now, with a scale factor of 2/3, that is
(6in * 2/3)(3in * 2/3) = (6in)(3in)(2/3)(2/3) = 18in^2 * 4/9 = 8 in^2
(2/3 length)(2/3 width) = (2/3)(2/3)(length*width) = (2/3)^2 * old area
same for volume, using 3 dimensions.
If you carry the units (in) with the values, this becomes clear.
If the old area is 18 in^2, that might be 6in * 3in
Now, with a scale factor of 2/3, that is
(6in * 2/3)(3in * 2/3) = (6in)(3in)(2/3)(2/3) = 18in^2 * 4/9 = 8 in^2
ok i kind of get it i thank you so much vary few people will help me anymore so thank you so much
1 answer