Question

What’s the height of the can?

Answer 1

Answer:

5 inches

Step-by-step explanation:

The formula to find the surface area of a cylinder is A = 2πrh + 2πr²  

Since we need the height we will need to solve for h

• First we can subtract 2πr² from both sides to get A - 2πr² = 2πrh
• Then we can divide both sides by 2πr to get $h=\frac{A-2\pi r^{2} }{2\pi r}$

Now we can plug in our known values and solve for h

• Here we were given the diameter, d, however this formula is in terms of the radius, r.
• The diameter is equivalent to double the radius, d = 2r
• Therefore the radius is equivalent to half the diameter, $r=\frac{1}{2} d$
• Plugging in d to solve for r we get $r=\frac{1}{2}(2)$ which simplifies to r = 1

The two variables for this equation we have no obtained, A = 12π and r = 1, so we can plug them into our equation to solve for the height

• $h=\frac{12\pi -2\pi (1)^{2} }{2\pi (1)}=h=\frac{12\pi -2\pi }{2\pi }=\frac{10\pi }{2\pi } =5$
• The height is 5 inches