Geometric Modeling Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
A can of soup is modelled as a cylinder. The can is 1212 cm tall and 77 cm in diameter. Calculate the volume of soup and the total surface area of metal needed to make the can.

Solution

  1. 1
    Step 1: Radius r=3.5r = 3.5 cm, height h=12h = 12 cm.
  2. 2
    Step 2: Volume =ฯ€r2h=ฯ€(3.5)2(12)=147ฯ€โ‰ˆ461.8= \pi r^2 h = \pi (3.5)^2 (12) = 147\pi \approx 461.8 cm3^3.
  3. 3
    Step 3: Total surface area =2ฯ€r2+2ฯ€rh=2ฯ€(3.5)2+2ฯ€(3.5)(12)=24.5ฯ€+84ฯ€=108.5ฯ€โ‰ˆ340.8= 2\pi r^2 + 2\pi r h = 2\pi(3.5)^2 + 2\pi(3.5)(12) = 24.5\pi + 84\pi = 108.5\pi \approx 340.8 cm2^2.

Answer

Volume โ‰ˆ461.8\approx 461.8 cm3^3; surface area โ‰ˆ340.8\approx 340.8 cm2^2.
The cylinder is a practical geometric model for cans, pipes, and tanks. Volume gives capacity and surface area gives material needed. These computations are directly applicable in manufacturing and packaging design.

About Geometric Modeling

Using geometric shapes and their relationships to represent, approximate, and analyze real-world objects and situations.

Learn more about Geometric Modeling โ†’

More Geometric Modeling Examples

Example 1 easy

A garden is modelled as a rectangle [formula] m long and [formula] m wide. Calculate the area to be

Example 3 easy

A triangular warning sign has a base of [formula] cm and height of [formula] cm. What area of reflec

Example 4 hard

A swimming pool has a rectangular flat bottom ([formula]) with a semicircular end on each short side

โ† All Geometric Modeling Examples Geometric Modeling Concept

Related Concepts

Basic Shapes