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Question bank: Spatial Geometry: Metric Relations of the Cylinder

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Question 1:

Very Hard

A revolution cylinder has a generatrix of 10 cm and a base radius of 3 cm. An ant starts walking in a straight line on the bottom base of the cylinder at a distance of 1 cm from the farthest point from the axis of rotation. The ant walks on the surface of the cylinder, always maintaining the same distance from the axis, and stops at the diametrically opposite point on the upper base. What is the total distance traveled by the ant? Consider that the surface of the cylinder is smooth and the ant cannot fly or dig. Additionally, it always maintains a distance of 1 cm from the axis of rotation of the cylinder.

Spatial Geometry: Metric Relations of the Cylinder

Multidisciplinary Question

Question 2:

Medium

A manufacturer of cans for canned food needs to design a new cylindrical can for a new product, respecting the following dimensions: the can must have a diameter of 12 cm and a height of 20 cm.

Spatial Geometry: Metric Relations of the Cylinder

Question 3:

Medium

A manufacturer of aluminum cans develops a new packaging model for a soda brand. The can has the shape of a right cylinder, with a radius of 3 cm and a height of 12 cm. (a) Calculate the distance between the center of the bottom base and a specific point on the edge of the top base, knowing that this point is on the same vertical line that passes through the center of the bottom base. (b) Determine the lateral area of the can. (c) If a straight cut is made on the can, connecting the center of the bottom base to the specific point on the edge of the top base and the can is unrolled until it becomes flat, determine the dimensions of this rectangle.

Spatial Geometry: Metric Relations of the Cylinder

Question 4:

Medium

You have been hired to design a cylindrical soda can with a height of 12 cm and a base diameter of 6 cm. Now with the can ready, you want to measure the distance between two points at the ends of the cylinder bases, one point at the center of the bottom base and the other point at the edge of the top base. What is this distance?

Spatial Geometry: Metric Relations of the Cylinder

Question 5:

Medium

Spatial Geometry: Metric Relations of the Cylinder

Contextualized Question

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