DAV Class 8 Maths Chapter 2 Enrichment Question
Cubes and Cube Roots Enrichment Question
1. Find the cube root of 4741632 by estimation.
Solution
\[ \begin{aligned} \text{II} \ \ \quad & \quad \, \, \, \text{I} \\ 4741 \quad & \quad 632 \\ \end{aligned} \] \[ \begin{aligned} \text{In the first group } 632 & \text{ has 2 in unit place.} \\ & 8^3 = 512 \\ \therefore \text{ One's place } & = 8 \\ \\ \end{aligned} \] \[ \begin{aligned} & \text{From the second group } 4741 \\ & \text{We know that } \\ & 4096 < 4741 < 4913 \\ & 16^3 < 10 < 17^3 \\ \therefore \, & \, \text{ Tens's place } = 16 \\ \\ &\sqrt[3]{4741632} = 168 \end{aligned} \]
Answer \( \color{red} \sqrt[3]{4741632} = 168 \)
2. Find the volume of a cube whose surface area is \( 150 \ m^2 \)
Solution
\[ \begin{aligned} \text{Surface area of a cube} & = 150 \ m^2 \\ \color{magenta} \text{Surface area of a cube} & = \color{magenta} 6 \times (Side)^2 \\ 6 \times (Side)^2 & = 150 \\ (Side)^2 & = \frac{\cancel{150}^{25}}{\cancel6_1} \\ (Side)^2 & = 25 \\ Side & = \sqrt{25} \\ Side & = 5 \ m \\\\ \color{magenta} \text{Volume of the cube} & = \color{magenta} (Side)^3 \\ & = (5 \ m)^3 \\ & = 125 \ m^3 \\ \end{aligned} \]
Answer Volume of the cube \( = \color{red} 125 \ m^3 \)