Step-by-step explanation: To find the surface area of the replica, we need to determine the dimensions of the replica first.
Given that the original sculpture is 21 m tall with a base of 9 m by 6 m, we can calculate its surface area.
The surface area of a rectangular prism can be found using the formula:
Surface Area = 2lw + 2lh + 2wh
where l is the length, w is the width, and h is the height of the prism.
For the original sculpture, the surface area would be:
Surface Area = 2(9)(6) + 2(9)(21) + 2(6)(21)
Simplifying, we have:
Surface Area = 108 + 378 + 252
Surface Area = 738 square meters
Now, we are asked to make a replica that will fit into a space that is 3 times smaller.
To find the dimensions of the replica, we need to divide the dimensions of the original sculpture by 3.
The height of the replica would be 21 m / 3 = 7 m.
The base of the replica would be 9 m / 3 = 3 m by 6 m / 3 = 2 m.
Now, we can find the surface area of the replica using the same formula.
Surface Area of the replica = 2(3)(2) + 2(3)(7) + 2(2)(7)
Simplifying, we have:
Surface Area of the replica = 12 + 42 + 28
Surface Area of the replica = 82 square meters
Therefore, the surface area of the replica would be 82 square meters.