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A right cylinder has a base area of 16 square inches and a height of 8 inches. Which shape does not have the same volume as the right cylinder? A. A right cylinder with a radius of 2 inches and a height of 32 inches. C. A cone with a base area of 16 square inches and a height of 24 inches. B. An oblique cylinder with a radius of 4 inches and a height of 8 inches. D. A cone with a radius of 4 inches and a height of 32 inches.

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Final Answer:

The shape that does not have the same volume as the given right cylinder is D. A cone with a radius of 4 inches and a height of 32 inches.

Step-by-step explanation:

The volume of a cylinder is given by the formula V_cylinder = πr²h, where r is the radius and h is the height. The initial right cylinder has a base area of 16 square inches and a height of 8 inches. Its volume is calculated as V₁ = π * (r₁)² * h₁, where the base area gives r₁ = √(16/π) = 4 inches. Therefore, V₁ = π * (4)² * 8 = 128π cubic inches.

Comparing this with the options:

A right cylinder with a radius of 2 inches and a height of 32 inches: V₂ = π * (2)² * 32 = 128π cubic inches. This option has the same volume as the given cylinder.

A cone with a base area of 16 square inches and a height of 24 inches: The formula for the volume of a cone is V_cone = 1/3 * π * r² * h. Using the given base area, r₃ = √(16/π) = 4 inches. So, V₃ = 1/3 * π * (4)² * 24 = 128π cubic inches. This option also has the same volume as the given cylinder.

An oblique cylinder with a radius of 4 inches and a height of 8 inches: V₄ = π * (4)² * 8 = 128π cubic inches. This option has the same volume as the given cylinder.

A cone with a radius of 4 inches and a height of 32 inches: V₅ = 1/3 * π * (4)² * 32 = 256π cubic inches. This option has a different volume (larger) compared to the initial cylinder, thus not having the same volume as the given right cylinder.

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