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
surface area will be in ratio of 2/3 of the original, and volume will be in the ratio of (2/3)^2 or 4/9 of 6
bobpursley
i have no clue what that means
I am not going to give you the answer, it is apparent from your posts, you think stealing answers is what you need.
To find the surface area and volume of the similar solid, we first need to understand the relationship between the dimensions of the original solid and the corresponding dimensions of the similar solid.
The ratio of corresponding dimensions of similar solids is the same for length, width, and height. In this case, the ratio is given as 2/3, which means that the corresponding dimensions of the similar solid are two-thirds the size of the corresponding dimensions of the original solid.
Let's denote the dimensions of the original solid as length (L), width (W), and height (H), and the corresponding dimensions of the similar solid as L', W', and H'.
We are given that the surface area (S.A.) of the original solid is 18 in.², so we can write the equation:
S.A. = 2(LW + LH + WH) = 18
We are also given that the volume (V) of the original solid is 6 in.³, so we can write the equation:
V = LWH = 6
Since the corresponding dimensions of the similar solid are two-thirds the size of the original solid, we have the equations:
L' = (2/3)L
W' = (2/3)W
H' = (2/3)H
Now, let's find the surface area and volume of the similar solid.
The surface area (S.A.') of the similar solid can be calculated by using the corresponding dimensions:
S.A.' = 2(L'W' + L'H' + W'H')
= 2((2/3)L(2/3)W + (2/3)L(2/3)H + (2/3)W(2/3)H)
= 2(4/9)LWH
= (8/9)(LWH)
= (8/9)(6)
= 48/9
= 16/3
= 5.3 repeating (approximately)
Therefore, the surface area of the similar solid is approximately 5.3 in.².
The volume (V') of the similar solid can be calculated using the corresponding dimensions:
V' = L'W'H'
= [(2/3)L][(2/3)W][(2/3)H]
= (2/3)³LWH
= (2/3)³(6)
= 8/27(6)
= 48/27
= 16/9
= 1.7 repeating (approximately)
Therefore, the volume of the similar solid is approximately 1.7 in.³.
So, the correct answer is: S.A. = 5.3 in.²; V = 1.7 in.³.