Rectangular prism
A
has a surface area of 25 square units and rectangular prism
B
has a surface area of 100 square units. Which statement accurately compares the dimensions of prism
A
to those of prism
B
?(1 point)
The surface area of a rectangular prism is determined by adding up the areas of all its faces. The formula for the surface area of a rectangular prism is:
SA = 2lw + 2lh + 2wh
Let's assume that the length, width, and height of prism A are a, b, and c respectively.
Therefore, the surface area of prism A, using the formula above, is:
25 = 2ab + 2ac + 2bc
Now let's assume that the length, width, and height of prism B are x, y, and z respectively.
Therefore, the surface area of prism B, using the formula above, is:
100 = 2xy + 2xz + 2yz
To compare the dimensions of prism A to those of prism B, we can set up a ratio:
(2ab + 2ac + 2bc) / (2xy + 2xz + 2yz) = 25/100
Simplifying the ratio gives:
(ab + ac + bc) / (xy + xz + yz) = 1/4
Therefore, the ratio of the dimensions of prism A to those of prism B is 1:4.
A triangular prism has a surface area of
486
in.
2
. If it were dilated using a scale factor of
1
3
, what would the new surface area be?(1 point)
To find the new surface area of the dilated triangular prism, we need to square the scale factor and multiply it by the original surface area.
The scale factor is 1/3, so the squared scale factor is (1/3)^2 = 1/9.
Therefore, the new surface area is (1/9) * 486 = 54 in^2.