Question 23 of 29intermediate🔧 ApplyShort Answer2 marks

Find the number of cubes with 1 digit, 2 digits, and 3 digits?

Correct Answer

Step 1: 1-digit cubes: 1³ = 1 2³ = 8 ∴ 2 cubes with 1 digit (1 and 8)

Step 2: 2-digit cubes: 3³ = 27 4³ = 64 ∴ 2 cubes with 2 digits (27 and 64)

Step 3: 3-digit cubes: 5³ = 125 6³ = 216 7³ = 343 8³ = 512 9³ = 729 ∴ 5 cubes with 3 digits (125, 216, 343, 512, and 729)

Answer: There are 2 cubes with 1 digit (1 and 8), 2 cubes with 2 digits (27 and 64), and 5 cubes with 3 digits (125, 216, 343, 512, and 729).

Exercise: Cubic Numbers | Q: 12 | (Page Page 13)
For More Understanding

Explanation

The chapter asks students to explore the distribution of cubes by number of digits. By calculating cubes and counting digits, we find: 1³ = 1 (1 digit), 2³ = 8 (1 digit), 3³ = 27 (2 digits), 4³ = 64 (2 digits), 5³ = 125 (3 digits), through 9³ = 729 (3 digits).

Solution Steps

  1. Step 1: 1-digit cubes: 1³ = 1, 2³ = 8 → 2 cubes

  2. Step 2: 2-digit cubes: 3³ = 27, 4³ = 64 → 2 cubes

  3. Step 3: 3-digit cubes: 5³ = 125, 6³ = 216, 7³ = 343, 8³ = 512, 9³ = 729 → 5 cubes

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