The largest possible right circular cylinder is cm out from a wooden cube of edge 7 cm. Find the volume of the cube left over after cutting the cylinder (in cm). (Use π = $\frac{22}{7}$)
Answer & explanation
Correct answer: option 1
We know that,
Volume of cube = side3
Volume of cylinder = πr2h
We have,
Edge of cube = 7 cm
Volume of cube = 73 = 343 cm3
When the largest possible right circular cylinder is cut out from a wooden cube then,
Height of cylinder = Edge of cube = 7 cm
Radius of cylinder = \(\frac{7}{2}\)cm
Volume of cylinder = π × r2 × h = \(\frac{22}{7}\) × \(\frac{7}{2}\) × \(\frac{7}{2}\) × 7 = 269.5 cm3
Remaining volume = 343 - 269.5 = 73.5 cm3