Question

12. The surface area of the soup can below is 51.84 in. If the

diameter of the can is 3 inches, find the height of the can.

Given: r=1.5


Given: 51.84=2pi(1.5)(h)+2pi(1.5squared)

Answer 1

Answer:

The height of the can is 4 inches.

Step-by-step explanation:

Cylinder:

• It is a three dimension shape.
• The lateral surface area is = 2πrh, r= radius, h= height.
• The total surface area is= (2πrh+2πr²)=2πr(r+h)
• The volume is = πr²h.

Given that, the surface area of the soup can is 51.84 in².

The diameter of the can is 3 inches.

Then, radius of the can $=\frac{Radius}{2}$

                                      $=\frac32$ inches

                                      =1.5 inches

Total surface area of the cone is = 2πrh+2πr²

                                                      $=2\pi (1.5)h+2\pi (1.5)^2$ in².

                                                      $=2\pi (1.5)(h+1.5)$  in².

                                                      =3π(h+1.5)  in².

So,

3π(h+1.5)=51.84

$\Rightarrow (h+1.5)=\frac{51.84}{3\pi}$

$\Rightarrow h=\frac{51.84}{3\pi}-1.5$

⇒h=5.5-1.5

⇒h=4 inches

The height of the can is 4 inches.