Math Problem Statement

Sam buys a fish tank in the shape of a cuboid with dimensions 100 cm by 30 cm by 30 cm. He wants to know if he can keep 36 small fish in it, knowing that 1000 cm³ = 1 litre, 4.5 litres = 1 gallon, and that he can keep 2 small fish per gallon of water. Is he correct?

Solution

To solve this problem, we need to:

  1. Calculate the volume of the tank in cubic centimeters.
  2. Convert the volume from cubic centimeters to gallons.
  3. Determine how many fish Sam can keep based on the number of gallons.

Step 1: Calculate the Volume of the Tank

The volume of a cuboid is calculated using the formula:

Volume=length×width×height\text{Volume} = \text{length} \times \text{width} \times \text{height}

Given:

  • Length = 100 cm
  • Width = 30 cm
  • Height = 30 cm

[ \text{Volume} = 100 , \text{cm} \times 30 , \text{cm} \times

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Math Problem Analysis

Mathematical Concepts

Volume of a Cuboid
Unit Conversion
Ratio and Proportion

Formulas

Volume of a Cuboid = length × width × height
Conversion of cm³ to litres: 1000 cm³ = 1 litre
Conversion of litres to gallons: 4.5 litres = 1 gallon

Theorems

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Suitable Grade Level

Grades 5-7