Considering the cube with dimensions given in this problem, we have that:
a) The volume after t hours is given by: V(t) = (0.5t + 4)³.
b) The surface area after t hours is given by: A(t) = 6(0.5t + 4)².
c) The surface area will equal 294 m² after 6 hours.
<h3>What are the volume and the surface area of a cube</h3>
Considering a cube of side length s, we have that:
For this problem, the side length after t hours is given by:
s(t) = 0.5t + 4.
Hence, the volume after t hours is given by:
V(t) = (0.5t + 4)³.
Also applying the formula, the surface area after t hours is given by:
A(t) = 6(0.5t + 4)².
The surface area will be equals to 294 m² when:
A(t) = 294.
Hence:
6(0.5t + 4)² = 294
(0.5t + 4)² = 294/6
(0.5t + 4)² = 49.
Applying the square root to both sides:
0.5t + 4 = 7
0.5t = 3
t = 6 hours.
More can be learned about the volume and the surface area of a cube at brainly.com/question/11436062
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