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The Height of a Right Circular Cylinder Is Increasing at the Rate

Question 74

Multiple Choice

The height of a right circular cylinder is increasing at the rate of 4 cm/s and its radius is decreasing at the rate of 2 cm/s. At what rate is the lateral surface area of the cylinder changing when the height is 3 centimetres and the radius is 1 centimetre?
The lateral surface area of a cylinder of base radius r and height h is given by S = 2 π\pi r h


A) decreasing at 16 π\pi  The height of a right circular cylinder is increasing at the rate of 4 cm/s and its radius is decreasing at the rate of 2 cm/s. At what rate is the lateral surface area of the cylinder changing when the height is 3 centimetres and the radius is 1 centimetre? The lateral surface area of a cylinder of base radius r and height h is given by S = 2  \pi r h A)  decreasing at 16  \pi    /s B)  decreasing at 4  \pi   /s C)  increasing at 4  \pi   /s D)  increasing at 20  \pi    /s E)  increasing at 16  \pi    /s /s
B) decreasing at 4 π\pi  The height of a right circular cylinder is increasing at the rate of 4 cm/s and its radius is decreasing at the rate of 2 cm/s. At what rate is the lateral surface area of the cylinder changing when the height is 3 centimetres and the radius is 1 centimetre? The lateral surface area of a cylinder of base radius r and height h is given by S = 2  \pi r h A)  decreasing at 16  \pi    /s B)  decreasing at 4  \pi   /s C)  increasing at 4  \pi   /s D)  increasing at 20  \pi    /s E)  increasing at 16  \pi    /s /s
C) increasing at 4 π\pi  The height of a right circular cylinder is increasing at the rate of 4 cm/s and its radius is decreasing at the rate of 2 cm/s. At what rate is the lateral surface area of the cylinder changing when the height is 3 centimetres and the radius is 1 centimetre? The lateral surface area of a cylinder of base radius r and height h is given by S = 2  \pi r h A)  decreasing at 16  \pi    /s B)  decreasing at 4  \pi   /s C)  increasing at 4  \pi   /s D)  increasing at 20  \pi    /s E)  increasing at 16  \pi    /s /s
D) increasing at 20 π\pi  The height of a right circular cylinder is increasing at the rate of 4 cm/s and its radius is decreasing at the rate of 2 cm/s. At what rate is the lateral surface area of the cylinder changing when the height is 3 centimetres and the radius is 1 centimetre? The lateral surface area of a cylinder of base radius r and height h is given by S = 2  \pi r h A)  decreasing at 16  \pi    /s B)  decreasing at 4  \pi   /s C)  increasing at 4  \pi   /s D)  increasing at 20  \pi    /s E)  increasing at 16  \pi    /s /s
E) increasing at 16 π\pi  The height of a right circular cylinder is increasing at the rate of 4 cm/s and its radius is decreasing at the rate of 2 cm/s. At what rate is the lateral surface area of the cylinder changing when the height is 3 centimetres and the radius is 1 centimetre? The lateral surface area of a cylinder of base radius r and height h is given by S = 2  \pi r h A)  decreasing at 16  \pi    /s B)  decreasing at 4  \pi   /s C)  increasing at 4  \pi   /s D)  increasing at 20  \pi    /s E)  increasing at 16  \pi    /s /s

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