Question

The volume V of a solid right circular cylinder is given by V = πr2h where r is the radius of the cylinder and h is its height. A soda can has inner radius r = 1.5 inches, height h = 6 inches, wall thickness 0.04 inches, and top and bottom thickness 0.07 inches. Use linearization to compute the volume, in cubic inches, of metal in the walls and top and bottom of the can. Give your answer to 2 decimal places.

Answer 1

Answer:

8.20in³

Step-by-step explanation:

Given V = πr²h

r is the radius = 1.5in

h is the height = 6in

thickness of wall of the cylinder dr = 0.04in

top and bottom thickness dh 0.07in+0.07in = 0.14in

To compute the volume, we will find the value of dV

dV = dV/dr • dr + dV/dh • dh

dV/dr = 2πrh

dV/dh = πr²

dV = 2πrh dr + πr² dh

Substituting the values into the formula

dV = 2π(1.5)(6)•(0.04) + π(1.5)²(6) • 0.14

dV = 2π (0.36)+π(1.89)

dV = 0.72π+1.89π

dV = 2.61π

dV = 2.61(3.14)

dV = 8.1954in³

Hence volume, in cubic inches, of metal in the walls and top and bottom of the can is 8.20in³ (to two dp)