24. If the scale factor of two similar solids is 4:17, what is the ratio of their corresponding areas and volumes? (1 point)
4:289 and 17:4,913
8:34 and 12:51
16:289 and 64:4,913
64:4,913 and 16:289
25. The volumes of two similar solids are 1,728 m3 and 343 m3. The surface area of the larger solid is 576 m2. What is the surface area of the smaller solid? (1 point)
196 m2
76 m2
1,372 m2
392 m2
24. The ratio of the corresponding areas can be found by squaring the scale factor, and the ratio of the corresponding volumes can be found by cubing the scale factor.
The given scale factor is 4:17, so the squared scale factor is (4^2):(17^2) = 16:289.
The cubed scale factor is (4^3):(17^3) = 64:4913.
Therefore, the correct answer is 16:289 and 64:4,913.
25. To find the surface area of the smaller solid, we can use the ratio of their volumes.
The ratio of their volumes is 1,728 m3 : 343 m3, which simplifies to 8:1.
Since the surface area is directly proportional to the volume for similar solids, we can use the same ratio to find the surface area.
The surface area of the larger solid is 576 m2.
So, the surface area of the smaller solid can be found by multiplying the ratio (8:1) by the surface area of the larger solid:
(8/1) * 576 m2 = 4,608 m2
Therefore, the correct answer is 4,608 m2.
For question 24, we have two similar solids with a scale factor of 4:17. To find the ratio of their corresponding areas and volumes, we need to square the scale factor for the ratio of areas and cube it for the ratio of volumes.
So, let's calculate the ratio of areas.
The square of the scale factor 4:17 is (4^2):(17^2) which equals 16:289.
Now, let's calculate the ratio of volumes.
The cube of the scale factor 4:17 is (4^3):(17^3) which equals 64:4913.
Therefore, the correct answer is option: 16:289 and 64:4,913.
For question 25, we have the volumes of two similar solids as 1,728 m^3 and 343 m^3. The surface area of the larger solid is given as 576 m^2.
Since the volumes of similar solids are proportional to the cube of the scale factor, let's find the scale factor.
(1728^(1/3))/(343^(1/3)) equals 12/7.
Now, let's find the corresponding surface area for the smaller solid.
The surface area is proportional to the square of the scale factor.
(576 * (49/144)) equals 196 m^2.
Therefore, the surface area of the smaller solid is 196 m^2, so the correct answer is option: 196 m^2.
length scale = 4/17
area scale = 4^2/17^2 = 16/289
vol scale = 4^3/17^3 = 64/4913
x^3/y^3 = 1728/343 volume ratio
x^2/y^2 = 576/y^2 area ratio
x/y =(1728/343)^(1/3) = 5.0379^(1/3)
= 1.7143 length ratio
so
x^2/y^2 = 1.7143^2 = 2.939
so
2.939 = 576/y^2
y^2 = 196 meters^2