Answer:
Remaining piece of wood 385 cm³
Step-by-step explanation:
Given data
A cylinder is drilled out from a wooden cone
The radius and height of the cylinder is equals to half that of the cone
Dimensions of cone are
⇒ Radius OP = 7 cm , ⇒ Height OQ = 12 cm
⇒ then volume of cone = [tex]\frac{1}{3} \pi r^{2} h[/tex] = [tex]\frac{1}{3}[/tex] × [tex]\frac{22}{7}[/tex] × 7 × 7 ×12 =
= 22 × 7 × 4 = 616 cm³
Dimensions of cylinder are
⇒ half of that of the cone
⇒ radius of cylinder r = 7/2 = 3.5 cm
⇒ height of cylinder h = 12/2 = 6 cm
⇒ volume of the cylinder = [tex]\pi r^{2} h[/tex] = [tex]\frac{22}{7}[/tex] × 3.5 × 3.5 × 6
= 22 × 3.5 × 3 = 231 cm³
here we need to find the remaining piece of wood
⇒ Remaining piece of wood = volume of cone - volume of cylinder
= 616 cm³ - 231 cm³
= 385 cm³