Rupesh Pathak and Vaishali Bhatia Solutions for Chapter: Cubes and Cube Roots, Exercise 3: Exercise 3.1

If an edge of cube is of length $15 \mathrm{cm}$, then find its volume. If the answer is $k {\mathrm{cm}}^3$, find $k$.

Fill in the blanks:

                         $1^3=1$

                $1^3+2^3=(1+2{)}^2$

       $1^3+2^3+3^3=(1+2+3{)}^2$

                         $1^3+2^3+3^3+4^3=(.....................{)}^2$

                         $......................=(1+2+3+4+5+6{)}^2$

                         $1^3+2^3+3^3+4^3+5^3+6^3+7^3+8^3+9^3={(........................)}^2$

                         $....................$  $={(1+2+3+4+5+6+7+8+9+10)}^2$

Find the difference between ${51}^3 \text{and} {50}^3$

Find the difference between ${16}^3 \text{and} {15}^3$

Find the difference between ${100}^3 \text{and} {101}^3$

Find the difference between ${90}^3 \text{and} {91}^3$

Find the difference between ${150}^3 \text{and} {151}^3$

Find the difference between ${1001}^3 \text{and} {1000}^3$