# calculus

A cylinder is generated by rotating a rectangle with perimeter 12 in. about one of its sides.?
Express the volume of the cylinder as a function of x.
Find the approximate value of x that maximizes the volume. Then give the approximate maximum volume.

1. 👍 0
2. 👎 0
3. 👁 875
1. if the rectangle is rotated about the side with length x, then the height is 6-x.

v = pi x^2 (6-x) = pi(6x^2 - x^3)
dv/dx = pi(12x-3x^2) = pi*3x(4-x)

so, when x=4, v is max.

1. 👍 1
2. 👎 0
2. A right circular cone of height 24 cm has a curved surface area 550 Square CM it's volume is

1. 👍 0
2. 👎 0
3. Find the missing dimension of the cylinder. The volume is 28 in3. Round your answer to the nearest whole number.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Math

The formula for the perimeter of a rectangle is P = 2l + 2w. The length of a rectangle is 3 times its width. Which expression represents the perimeter of the rectangle? Question 3 options: 2 + w(3w) 2 + w(w + 3) 2(3w) + 2w 2(w +

2. ### Calculus

A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 30ft, find the dimensions of the window so

3. ### Physics

A small metal cylinder rests on a circular turntable that is rotating at a constant speed. The small metal cylinder has a mass of 0.20kg, the coefficient of static friction between the cylinder and the turntable is 0.080, and the

4. ### physics

A small cylinder rests on a circular turntable that is rotating clockwise at a constant speed. The cylinder is at a distance of r = 12 cm from the center of the turntable. The coefficient of static friction between the bottom of

1. ### Math

Rectangle ABCD is similar to rectangle EFGH. If rectangle ABCD has sides that are 7 times greater than those of rectangle EFGH, what is the relationship between the perimeters of the rectangles? A. The perimeter of rectangle EFGH

2. ### basic geometric

10. a rectangle has width the same as a side of a square whose perimeter is 20m. the length of the rectangle is 9m. find the perimeter of this rectangle. 34. The width of a rectangular picture is one-half the length. The perimeter

3. ### Math

The sides of a rectangle are increased by a scale factor of 4. The perimeter of the smaller rectangle is 20 cm. What is the perimeter of the larger rectangle?

4. ### Algebra

What is the length of the original rectangle? The perimeter of a rectangle is equal to 40. If the length is halved and the width is divided by 3, the new perimeter is decreased by 24. Select one: a. 12 b. 8 c. 4 d. 16

1. ### math

the area of a certain rectangle is 288 yd squared. the perimeter is 68 yards. f you double the length and width what will be the area and perimeter of the new rectangle

2. ### math

the length of a rectangle is 5 ft more than twice the width. a)if x represents the width of the rctangle, represent the perimeter of the rectangle in terms of x. b) if the perimeter if the rectangle is 2 ft more than eight times

3. ### Math

The length of a rectangle is 5 cm greater than it width. The perimeter is 58 cm. What are the dimension of the rectangle? I know the formula for Triangle Perimeter is 2(L+W) and the L is +5 more than the W but I can't write the

4. ### Math,Ratio

the length of a rectangle is 6times as long as its breadth. a.) what fraction of the perimeter of the rectangle is the length of the rectangle? b.) find the ratio of the length of the rectangle to its breadth and to its perimeter.