Answer:
10,596 cubic inches
Explanation:
The shape of the prism with which the sand castle can be modelled = Square prism
The arrangement of the square prism = One on top of the other
The given height of each prism, h = 6 inches
The side length of the base of the bottom prism, s₄ = 30 inches
The side length of the base of the other prism = The side length of the base of the prism below each prism - 7 inches
Therefore;
The side length of a prism = 7 inches + The side length of the prism above it
Given that the side length of the base prism (The fourth prism), s₄ = 30 inches
The side length of the prism, directly above the base prism (The fourth prism), s₃ = (30 - 7) inches = 23 inches
The side length of the prism, directly above the third prism (The second prism), s₃ = (23 - 7) = 16 inches
The side length of the top most prism, s₁ = (16 - 7) inches = 9 inches
The volume of the sand castle, V = h × (s₄² + s₃² + s₂² + s₁²)
∴ V = 6 × (30² + 23² + 16² + 9²) = 10,596
The volume of the sand castle, V = 10,596 in.³