Ch 4 Rev Related Rates

(3 min) The top of a 25 foot ladder is sliding down a vertical wall at a constant rate of 3 feet per minute. When the top of the ladder is 7 feet from the ground, what is the rate of change of the distance between the bottom of the ladder and the wall?

• 7/8
• -7/8
• 7/24
• -7/24

Tags

CCSS.HSA.REI.C.6

CCSS.HSG.SRT.C.8

 (3 min) The volume of a cone of radius r and height h is given by v = (1/3) π r² h. If the radius and the height both increase at a constant rate of 1/2 centimeter per second, at what rate, in cubic centimeters per second, is the volume increasing when the height is 9 centimeters and the radius is 6 centimeters?

• 10π
• 24π
• 54π
• 108π

(3 min) The area of a circular region is increasing at a rate of 96 π square meters per second. When the area of the region is 64 π square meters, how fast, in meters per second, is the radius of the region increasing?

• 6
• 8
• 16
• 4√3

(3 min) If the base b of a triangle is increasing at a rate of 3 inches per minute while its height h is decreasing at a rate of 3 inches per minute, which of the following must be true about the area A of the triangle?

• Area is decreasing when b<h.
• Area is increasing when b<h.
• Area remains constant.
• Cannot be determined from the given information.

(3 min) The radius r of a sphere is increasing at the uniform rate of 0.3 inches per second. At the instant when the surface area S becomes 100 π square inches, what is the rate of increase, in cubic inches per second, in the volume V? SA = 4 π r² and V = (4/3) π r³

• 30π
• 10π
• 12π
• 25π

Tags

CCSS.HSG.GMD.A.3

(3 min) The radius of a circle is decreasing at a constant rate of 0.1 centimeter per seconds.  In terms of the circumference C, what is the rate of change of the area of the circle, in square centimeters per second?

• -0.1C
• -0.1²C
• -0.2 π C
• 0.1C

(3 min) The radius of a circle is increasing at a nonzero rate, and at a certain instant, the rate of increase in the area of the circle is numerically equal to the rate of increase in its circumference. At this instant, the radius of the circle is

• 1/π
• 1/2
• 2/π
• 1