Question

From a cube of edge 7m, a cylinder of maximum size is carved out. What will be the volume of the remaining material in cubic meter

Answer 1

The volume of the remaining material is 73.5 $m^{3}$

Step-by-step explanation:

When we carved out a cylinder of maximum size from a cube, the height of the cylinder will be equal to the edge of the cube and the radius of the cylinder will be equal to the half of the edge of the cube.

• Now, the edge of the cube (a) = 7 m
•     ∴ the height of the cylinder (h) = 7 m
•    and radius of the cylinder (r) = $\dfrac{7}{2}$  = 3.5 m
• So, volume of the cube = $a^{3}$ = $7^{3}$ = 343 $m^{3}$

     volume of the cylinder = $\pi$ × $r^{2}$ × h

                                            = $\dfrac{22}{7}$ × 3.5 × 3.5  × 7                ( $\pi$ = $\dfrac{22}{7}$ )

                                            = 269.5 $m^{3}$

∴ the volume of the remaining material = (volume of the cube) - (volume of the cylinder)

                                              = 343 - 269.5

                                              = 73.5 $m^{3}$

∴The volume of the remaining material is 73.5 $m^{3}$

Answer 2

The volume of the remaining material in cubic meter will be = 73.5 m³.

Step-by-step explanation:

The maximum size of the cylinder will have a height of 7 m and a diameter of 7 m.

So, its volume will be = $\pi r^{2} h = \frac{22}{7}\times 3.5^{2} \times 7 = 269.5$ m³.

Now, the volume of the cube of edge 7 m will be = (7 × 7 × 7) = 343 m³.

Therefore, the volume of the remaining material in the cubic meter will be = (343 - 269.5) = 73.5 m³. (Answer)