Question

A cylindrical bottle has a volume of 1,413 in3 and a radius of 5 inches. What is the height of the bottle?​

Answer 1

h = 17.9909 in

General Formulas and Concepts:

Symbols

• π (pi) ≈ 3.14

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Geometry

Volume of a Cylinder Formula: V = πr²h

• r is radius
• h is height

Explanation:

Step 1: Define

Identify variables

V = 1413 in³

r = 5 in

Step 2: Solve for h

1. Substitute in variables [Volume of a Cylinder Formula]: 1413 in³ = π(5 in)²h
2. Evaluate exponents: 1413 in³ = π(25 in²)h
3. [Division Property of Equality] Divide π on both sides: 449.772 in³ = (25 in²)h
4. [Division Property of Equality] Divide 25 on both sides: 17.9909 in = h
5. Rewrite: h = 17.9909 in