Question

A cereal company is designing containers for a new type of cereal. Each container will be shaped like either a rectangular prism or a cylinder and needs to have a volume of 258 3/4 cubic inches. In one design being considered for the container shaped like a cylinder, the container will have a height of 12 inches. What will be the radius of the container, to the nearest tenth of an inch?

a) 3.7 inches
b) 4.3 inches
c) 4.7 inches
d) 5.2 inches

Answer 1

To find the radius of the cylinder, use the formula for the volume of a cylinder: V = πr²h. Substitute the given values into the formula and solve for the radius. The radius of the cylinder, to the nearest tenth of an inch, is approximately 2.6 inches.

Step-by-step explanation:

To find the radius of the cylinder, we need to use the formula for the volume of a cylinder: V = πr²h. In this case, the volume is given as 258 3/4 cubic inches and the height is 12 inches. Substituting these values into the formula, we can solve for the radius:

258 3/4 = 3.142 × r² × 12

Divide both sides of the equation by 3.142 × 12 to isolate r²:

r² = 258.75 / (3.142 × 12)

r² ≈ 6.83

Take the square root of both sides to find the value of r:

r ≈ √6.83 ≈ 2.61

So, the radius of the cylinder, to the nearest tenth of an inch, is approximately 2.6 inches.