Question

A motor oil manufacturer is designing a new cylindrical can for its economy size. They want it to be 23 cm tall so it fits store shelves, and they want it to hold 2 liters of oil. What should the radius be?

Answer 1

To find the radius of a cylindrical oil can that is 23 cm tall and holds 2 liters, the formula V = πr²h is used. After setting up and solving the equation, the radius is found to be approximately 9.38 cm.

Step-by-step explanation:

To determine the radius of a new cylindrical oil can that is 23 cm tall and holds 2 liters of oil, we must use the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height. Since 1 liter equals 1,000 cm³ (or 0.001 m³), 2 liters is equivalent to 2,000 cm³.

First, we set up the equation using the given volume (V) and height (h):

2,000 cm³ = πr²(23 cm)

Next, we solve for r²:

r² = 2,000 cm³ / (π × 23 cm)

r² = 2,000 cm³ / (3.14159 × 23 cm)
= 87.949 cm²

Now we find the radius (r) by taking the square root of r²:

r = √(87.949 cm²)
= 9.382 cm

So, for the cylindrical can to hold 2 liters of oil and be 23 cm tall, the radius should be approximately 9.38 cm.

Answer 2

The radius of the cylindrical can should be approximately 6.55 cm.

Step-by-step explanation:

To find the radius of the cylindrical can, we need to use the formula for the volume of a cylinder, which is V = πr²h.

In this case, the height (h) is given as 23 cm and the volume (V) is given as 2 liters. Since 1 liter is equal to 1000 cm³, we can convert the volume to cm³ by multiplying it by 1000.

So, the equation becomes 2 * 1000 = 3.142 * r² * 23. Solving for r, we find that the radius should be approximately 6.55 cm.