We need to find the surface area of a rectangular prism with dimensions 5, 4, and 3 units. The surface area formula is SA = 2(lw + lh + wh) where l, w, h are the dimensions. Substituting: SA = 2(5×4 + 5×3 + 4×3) = 2(20 + 15 + 12) = 2(47) = 94 square units. This accounts for all six rectangular faces of the prism.

This is a cylinder volume question testing inverse use of the volume formula. Choice A (3) is correct — V = πr²h → 72π = πr²(8) → divide both sides by π: 72 = 8r² → r² = 9 → r = 3 inches. Choice B (4.5) results from dividing 72 by 8 to get 9, then halving instead of taking the square root: 9/2 = 4.5. Choice C (6) may result from computing 72/8 = 9 and then computing √(9 × 4) = 6 — an incorrect extra step. Choice D (9) correctly solves r² = 9 but reports r² rather than r — forgetting to take the square root. Pro tip: When solving V = πr²h for r, cancel π first (it divides out cleanly), then divide by h to isolate r², and THEN take the square root. Write out each step to avoid stopping at r².

This is a volume and displacement question testing Archimedes' principle (water displacement). Choice C (240) is correct — the volume of the submerged rock equals the volume of water displaced. The water level rose 2 inches across a 12 × 10 inch base. Volume displaced = 12 × 10 × 2 = 240 cubic inches = volume of rock. Choice A (24) adds the dimensions instead of multiplying: 12 + 10 + 2 = 24. Choice B (120) uses only the base area without the height rise: 12 × 10 = 120 — finding the base area but not the volume of displaced water. Choice D (480) doubles the correct answer — perhaps computing 12 × 10 × 4 (using 4 instead of 2) or multiplying the result by 2. Pro tip: When an object is submerged in a tank, the volume of the displaced water equals the volume of the object. Displaced water forms a rectangular prism with the tank's base dimensions and the height equal to the water rise. Volume = length × width × rise = 12 × 10 × 2 = 240. This principle applies whenever the tank has uniform (rectangular) cross-section.

We need to find the volume of a cone with radius 3 units and height 12 units. The volume formula for a cone is V = (1/3)πr²h. Substituting r = 3 and h = 12: V = (1/3) × π × (3²) × 12 = (1/3) × π × 9 × 12 = (1/3) × 108π = 36π cubic units. Choice D forgot to apply the 1/3 factor specific to cone volume.

We need to find the volume of a cone with radius 3 units and height 12 units. The volume formula for a cone is V = (1/3)πr²h. Substituting r = 3 and h = 12: V = (1/3) × π × (3²) × 12 = (1/3) × π × 9 × 12 = (1/3) × 108π = 36π cubic units. Choice B forgot to multiply by 1/3, giving the volume of a cylinder instead.

We need to find the surface area of a rectangular prism with length 9, width 4, and height 2 units. The surface area formula is SA = 2(lw + lh + wh). Substituting: SA = 2(9×4 + 9×2 + 4×2) = 2(36 + 18 + 8) = 2(62) = 124 square units. Choice A incorrectly calculated only the sum of areas without doubling for opposite faces.

This is finding the side length of a cube given surface area 54 square units. The surface area formula for a cube is SA = 6s², where s is the side length. Setting up: 54 = 6s², so s² = 54/6 = 9, therefore s = 3 units. The cube has six equal square faces.

The solid is a cube with side length 7 units, and we need to find its surface area. The formula for the surface area of a cube is SA = 6s², where s is the side length. Substituting the value, SA = 6(7)² = 6(49). This calculates to 294 square units. The cube has six square faces, each with area s². A distractor like 343 is the volume (s³), not the surface area.

We need to find the volume of a cone with radius 3 units and height 12 units. The volume formula for a cone is V = (1/3)πr²h. Substituting r = 3 and h = 12: V = (1/3)π(3²)(12) = (1/3)π(9)(12) = (1/3)π(108) = 36π cubic units.

The solid is a square pyramid with a square base of side length 6 units and height 9 units, and we are finding its volume. The formula for the volume of a pyramid is V = (1/3) × base area × height, where the base area is s² for a square base. Substituting s = 6 and height = 9, base area = 36, so V = (1/3) × 36 × 9. Then, 36 × 9 = 324, and (1/3) × 324 = 108 cubic units. Choice B, 324 cubic units, might result from omitting the 1/3 factor, treating it like a prism volume.