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
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...
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
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
ok i kind of get it i thank you so much vary few people will help me anymore so thank you so much
To find the surface area and volume of the similar solid, we can use the concept of scale factor. The scale factor is the ratio of corresponding dimensions of the two solids. In this case, the scale factor is 2/3.
Let's denote the surface area and volume of the original solid as SA1 and V1, respectively. The surface area and volume of the similar solid are denoted as SA2 and V2.
We are given that the surface area of the original solid is 18 in.2 (SA1 = 18 in.2) and its volume is 6 in.3 (V1 = 6 in.3).
To find the surface area of the similar solid (SA2), we can use the formula:
SA2 = (scale factor)^2 * SA1
Plugging in the given values:
SA2 = (2/3)^2 * 18 in.2
SA2 = (4/9) * 18 in.2
SA2 = 8 in.2
Therefore, the surface area of the similar solid is 8 in.2.
To find the volume of the similar solid (V2), we can use the formula:
V2 = (scale factor)^3 * V1
Plugging in the given values:
V2 = (2/3)^3 * 6 in.3
V2 = (8/27) * 6 in.3
V2 = 1.7 repeating in.3
Therefore, the volume of the similar solid is approximately 1.7 repeating in.3.
Hence, the correct answer is:
S.A. = 8 in.2; V = 1.7 repeating in.3.