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Original 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...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 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 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 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.
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 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 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 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.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
The surface area \( S \) of a rectangular prism can be expressed as:
\[
S = 2(lw + lh + wh)
\]
where \( l \), \( w \), and \( h \) are the length, width, and height of the prism, respectively.
When comparing two prisms, if the surface area of prism B is \( k \) times that of prism A (in this case, \( k = 4 \), since 100 is 4 times 25), we cannot directly deduce that the dimensions of prism B are \( k \) times the dimensions of prism A.
In fact, if the dimensions of prism A are scaled by a factor \( r \), the surface area scales by \( r^2 \). Thus, if the surface area of prism B is 4 times that of prism A, this suggests that the dimensions of prism B are scaled by a factor of:
\[
r^2 = 4 \implies r = 2
\]
Therefore, the dimensions of prism B are twice as large as those 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."
\[
S = 2(lw + lh + wh)
\]
where \( l \), \( w \), and \( h \) are the length, width, and height of the prism, respectively.
When comparing two prisms, if the surface area of prism B is \( k \) times that of prism A (in this case, \( k = 4 \), since 100 is 4 times 25), we cannot directly deduce that the dimensions of prism B are \( k \) times the dimensions of prism A.
In fact, if the dimensions of prism A are scaled by a factor \( r \), the surface area scales by \( r^2 \). Thus, if the surface area of prism B is 4 times that of prism A, this suggests that the dimensions of prism B are scaled by a factor of:
\[
r^2 = 4 \implies r = 2
\]
Therefore, the dimensions of prism B are twice as large as those 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."
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