Math Problem Statement

A can of beans has a height of 12 cm and a diameter of 7.6 cm. If you were to use the label that surrounds the can for advertising, how much surface area would you have to advertise on?

Solution

To find the surface area of the label that surrounds the can of beans, we need to calculate the lateral surface area of the cylinder.

Given:

  • Height of the can h=12cmh = 12 \, \text{cm}
  • Diameter of the can d=7.6cmd = 7.6 \, \text{cm}

First, we find the radius rr of the can: r=d2=7.6cm2=3.8cmr = \frac{d}{2} = \frac{7.6 \, \text{cm}}{2} = 3.8 \, \text{cm}

The lateral surface area AA of a cylinder is given by the formula: A=2πrhA = 2 \pi r h

Substitute the given values: A=2π×3.8cm×12cmA = 2 \pi \times 3.8 \, \text{cm} \times 12 \, \text{cm}

Perform the multiplication: A=2π×3.8×12A = 2 \pi \times 3.8 \times 12 A=2π×45.6A = 2 \pi \times 45.6 A=91.2πcm2A = 91.2 \pi \, \text{cm}^2

Using the value of π3.14159\pi \approx 3.14159: A91.2×3.14159A \approx 91.2 \times 3.14159 A286.48cm2A \approx 286.48 \, \text{cm}^2

Therefore, the surface area available for advertising on the label is approximately 286.48cm2\boxed{286.48 \, \text{cm}^2}.

Would you like any further details or have any questions?

Here are 5 questions you can ask:

  1. How do you calculate the volume of a cone?
  2. What is the formula for the surface area of a sphere?
  3. How do you solve systems of linear equations?
  4. Can you explain the concept of limits in calculus?
  5. How do you find the area of a trapezoid?

Tip: Always double-check the units and conversion factors when performing calculations to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Geometry
Surface Area
Cylinders

Formulas

Surface area of a cylinder: A = 2πrh

Theorems

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Suitable Grade Level

Grades 7-9