Question bank: Volume and Area: Cylinder

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Question 1:

Medium

Volume and Area: Cylinder

Contextualized Question

Question 2:

Medium

Volume and Area: Cylinder

Contextualized Question

Question 3:

Hard

A revolution cylinder is a solid whose lateral faces are two identical and parallel cylindrical surfaces and whose bases are two identical and parallel circular discs. An architecture student is designing a cylindrical water tower for a water reuse project in a community. The tower must have a water storage capacity of 5000 cubic meters. Additionally, the student wants to externally coat the tower with a material that costs R$ 10.00 per square meter. Considering that the tower should be as efficient as possible in terms of material usage for coating, the student wants to know what should be the height and radius of the tower to minimize the coating cost, knowing that the volume of a cylinder is given by V = π * r^2 * h and the surface area is given by A = 2 * π * r * (r + h). Based on these calculations and the cost function C = 10 * A, where C is the cost of the coating, determine the height and radius that minimize the coating cost.

Volume and Area: Cylinder

Multidisciplinary Question

Question 4:

Hard

In an ice cream factory, a cylindrical storage tank has a capacity of 500 liters of ice cream. The diameter of the cylinder base is 1.6 meters. In addition, the factory needs to replace the tank wall, which has a thickness of 5 centimeters. Considering that the tank is made of a homogeneous material and that the thickness of the new wall will be the same, calculate the area of the new wall that will be installed and the exact amount of material in square meters that will be used for this replacement.

Volume and Area: Cylinder

Contextualized Question

Calculus Question

Question 5:

Easy

What is the volume of a right cylinder with a height of 10cm and a base radius of 5cm?

Volume and Area: Cylinder

IARA TIP

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