A right circular cylinder is changing shape. The radius is decreasing at the rate of 2 inches/sec while it's height is increasing at the rate of 5 inches/sec. When the radius is 4 inches and the height is 6 inches, how fast is the volume changing? Round your answer to three decimal places

552.640in³/s

Step-by-step explanation:

Volume of a cylinder is expressed as;

dV/dr = 2πrh

dV/dr = 2π(4)(6)

dV/dr = 48(3.14)

dV/dr = 150.72in³/m

dV/dh = πr²

dV/dh = 3.14(4)²

dV/dh = 50.24

Given

dh/dt = 5in/s

dr/dt = 2in/s

Substitute into the dV/dt

dV/dt = 150.72(2)+50.24(5)

dV/dt = 301.44 + 251.2

dV/dt= 552.640in³/s

The volume is changing at the rate of  552.640in³/s

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.