Question
Similar Figures and Surface Area Quick Check 2 of 52 of 5 Items Question 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) Responses Since prism B’s surface area is 4 times as large as prism A’s surface area, prism B’s dimensions are half as large as prism A’s. Since prism upper B ’s surface area is 4 times as large as prism upper A ’s surface area, prism upper B ’s dimensions are half as large as prism upper A ’s. Since prism B’s surface area is 4 times as large as prism A’s surface area, prism B’s dimensions are 8 times as large as prism A’s. Since prism upper B ’s surface area is 4 times as large as prism upper A ’s surface area, prism upper B ’s dimensions are 8 times as large as prism upper A ’s. Since prism B’s surface area is 4 times as large as prism A’s surface area, prism B’s dimensions are 16 times as large as prism A’s. Since prism upper B ’s surface area is 4 times as large as prism upper A ’s surface area, prism upper B ’s dimensions are 16 times as large as prism upper A ’s. Since prism B’s surface area is 4 times as large as prism A’s surface area, prism B’s dimensions are twice as large as prism A’s. Since prism upper B ’s surface area is 4 times as large as prism upper A ’s surface area, prism upper B ’s dimensions are twice as large as prism upper A ’s. Skip to navigation page 17 of 17 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.
Answers
GPT-4o mini
To compare the dimensions of the rectangular prisms A and B based on their surface areas, we can utilize the relationship between the surface area and the dimensions of similar figures.
The surface area of a three-dimensional shape (such as a rectangular prism) is proportional to the square of its linear dimensions. This means that if the surface area of prism B is 4 times that of prism A, we can deduce the ratio of their dimensions.
Let’s denote the dimensions of prism A as \(d_A\) and the dimensions of prism B as \(d_B\).
Given:
- Surface area of prism A = 25 square units
- Surface area of prism B = 100 square units
Since \(100 = 4 \times 25\), we can find the ratio of the dimensions:
\[
\left( \frac{d_B}{d_A} \right)^2 = 4
\]
Taking the square root of both sides gives:
\[
\frac{d_B}{d_A} = 2
\]
This implies that each dimension of prism B is twice that of prism A.
Thus, the correct statement is:
"Since prism B’s surface area is 4 times as large as prism A’s surface area, prism B’s dimensions are twice as large as prism A’s."
This statement aligns with the proportional relationship we derived.
The surface area of a three-dimensional shape (such as a rectangular prism) is proportional to the square of its linear dimensions. This means that if the surface area of prism B is 4 times that of prism A, we can deduce the ratio of their dimensions.
Let’s denote the dimensions of prism A as \(d_A\) and the dimensions of prism B as \(d_B\).
Given:
- Surface area of prism A = 25 square units
- Surface area of prism B = 100 square units
Since \(100 = 4 \times 25\), we can find the ratio of the dimensions:
\[
\left( \frac{d_B}{d_A} \right)^2 = 4
\]
Taking the square root of both sides gives:
\[
\frac{d_B}{d_A} = 2
\]
This implies that each dimension of prism B is twice that of prism A.
Thus, the correct statement is:
"Since prism B’s surface area is 4 times as large as prism A’s surface area, prism B’s dimensions are twice as large as prism A’s."
This statement aligns with the proportional relationship we derived.