This problem asks for the volume expression of a cone-shaped ice cream cone. The solid is a right circular cone with radius 4 cm and height 9 cm. The volume formula for a cone is V = (1/3)πr²h, where r is the radius and h is the height. The correct expression is (1/3)π(4²)(9), which represents one-third of the volume of a cylinder with the same base and height. This formula accounts for the cone's tapering shape from base to apex. A common mistake is using the cylinder formula π(4²)(9), forgetting the factor of 1/3. Remember that a cone's volume is always one-third of a cylinder with the same dimensions.

This problem requires finding the volume of wax in a candle with a conical hole. The solid is a cylinder (radius 3 cm, height 14 cm) minus a cone (same radius 3 cm, depth 6 cm). The volume formula requires subtracting: V = cylinder volume - cone volume = πr²h - (1/3)πr²h. Applying: V = π(3)²(14) - (1/3)π(3)²(6) = 126π - 18π = 108π cm³. The subtraction accounts for the removed wax from the conical hole. Option C incorrectly adds the volumes instead of subtracting. When dealing with composite solids involving removal, subtract the volume of the removed portion from the original solid.

This problem involves finding the volume of a cylindrical can given its diameter. The solid is a right circular cylinder with diameter 10 cm and height 12 cm. Since the volume formula V = πr²h requires radius, we must first convert: radius = diameter/2 = 10/2 = 5 cm. Applying the formula: V = π(5)²(12) = π(25)(12) = 300π cubic centimeters. This represents the can's total capacity. A common mistake is using diameter directly in the formula, giving π(10)²(12) = 1200π, which is four times too large. Always convert diameter to radius before applying cylinder volume formulas.

This problem asks which expression represents the volume of a cylindrical candle. The solid is a cylinder with radius 5 cm and height 12 cm. The volume formula for a cylinder is V = πr²h, where r is the radius and h is the height. The correct expression is π(5²)(12) or π(25)(12). This formula gives the volume in cubic centimeters. Option A represents the lateral surface area formula (2πrh), not volume. To find volume, always use formulas that multiply three dimensions or include squared terms for circular shapes.

This problem requires finding the volume of a square pyramid. The solid is a square pyramid with base side length 8 m and height 15 m. The volume formula for a pyramid is V = (1/3)Bh, where B is the base area and h is the height. For a square base, B = s² = 8² = 64 m². Applying the formula: V = (1/3)(64)(15) = (1/3)(960) = 320 cubic meters. A common error is forgetting the factor of 1/3, which would give 960 m³ instead. When solving pyramid problems, remember that the volume is always one-third of the base area times the height.

Solving problems with volume formulas involves calculating the space occupied by three-dimensional solids using appropriate mathematical expressions. The solid in this problem is a right circular cone. The correct volume formula for a cone is V = (1/3)πr²h, where r is the radius and h is the height. Applying the formula with r = 4 cm and h = 12 cm gives the expression (1/3)π(4)²(12), matching choice B. This expression correctly computes the volume by accounting for the conical shape's one-third factor of a cylinder's volume. A common distractor misconception is using the cylinder volume formula without the one-third, as in choice A, which overestimates the volume. To transfer this strategy, always identify the solid as a cone before selecting and applying the volume formula.

Solving problems with volume formulas involves calculating the space occupied by three-dimensional solids using appropriate mathematical expressions. The solid in this problem is a right square pyramid. The correct volume formula for a pyramid is V = (1/3) B h, where B is the base area and h is the height. Applying the formula with base side 6 m (B = 36 m²) and h = 9 m gives V = (1/3)(36)(9) = 108 m³, matching choice B. This result correctly accounts for the pyramidal shape's volume being one-third of a prism with the same base and height. A common distractor misconception is omitting the one-third factor, as in calculating 36 × 9 = 324 m³ like choice A. To transfer this strategy, always identify the solid as a pyramid before selecting and applying the volume formula.

Solving problems with volume formulas involves calculating the space occupied by three-dimensional solids using appropriate mathematical expressions. The solid in this problem is a right circular cylinder. The correct volume formula for a cylinder is V = πr²h, where r is the radius and h is the height. Applying the formula with r = 2.5 in and h = 8 in gives the expression π(2.5)²(8), matching choice A. This expression accurately computes the volume based on the cylindrical dimensions. A common distractor misconception is using the lateral surface area formula, as in choice B, which calculates 2πr h instead of volume. To transfer this strategy, always identify the solid as a cylinder before selecting and applying the volume formula.

Solving problems with volume formulas involves calculating the space occupied by three-dimensional solids using appropriate mathematical expressions. The solid in this problem is a right circular cylinder. The correct volume formula for a cylinder is $V = \pi r^2 h$, where r is the radius and h is the height. Applying the formula with $r = 3 \text{ m}$ and $h = 10 \text{ m}$ gives $V = \pi(3)^2 (10) = 90\pi \text{ m}^3$. This result represents the maximum capacity of water the tank can hold when full, matching choice B. A common distractor misconception is using the surface area formula, such as choice D, which calculates $2\pi r h + 2\pi r^2$ instead of volume. To transfer this strategy, always identify the solid as a cylinder before selecting and applying the volume formula.

Solving problems with volume formulas involves calculating the space occupied by three-dimensional solids using appropriate mathematical expressions. The solid in this problem is a right circular cylinder. The correct volume formula for a cylinder is V = $\pi r^2 h$, where r is the radius and h is the height. Applying the formula with r = 3 cm and h = 12 cm gives V = $\pi(3)^2 (12) = 108\pi$ cm³, which shows claims A and B are justified while D is a valid property. However, claim C uses $2\pi r h$, the lateral surface area, incorrectly as volume, making it not justified and matching choice C. A common distractor misconception is confusing volume with surface area formulas, as seen in choice C. To transfer this strategy, always identify the solid as a cylinder before evaluating claims about its volume.