Question

A juice container shaped like a cylinder has a base radius of (5.64 , {cm}) and can hold (1500 , {cm}^3) of juice. The height of the juice container is closest to

a) (150 , {cm})
b) (15 , {cm})
c) (10 , {cm})
d) (1.5 , {cm})

Answer 1

The height of the cylinder-shaped juice container is closest to 15 cm, calculated by dividing the volume of the container by the base area using the formula for the volume of a cylinder.

Step-by-step explanation:

To find the height of a cylinder given its base radius and the volume, you can 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 we know that the base radius is 5.64 cm and the volume is 1500 cm³, we can arrange the formula to solve for the height h = V / (πr²).

First, calculate the base area of the cylinder: π × (5.64 cm)².

Next, divide the volume of the juice container by its base area to find the height. Using the given values:

V = 1500 cm³
A = π × (5.64 cm)² = 100.067904 cm² (approximately)
h = 1500 cm³ / 100.067904 cm² = 14.993 cm (approximately)

So, the height of the cylinder juice container is closest to 15 cm, which corresponds to option b) 15 cm.