Home › Kerala SSLC (Class 10) › mathematics › Cones › A cylindrical block of wood has base radius 15 c…
A cylindrical block of wood has base radius 15 cm and height 40 cm. The volume of the largest cone that can be carved out of it equals:
Answer & Solution
Correct answer: C.
1. The largest cone has the same base radius and height as the cylinder.
2. V_cone = (1/3) π r² h = (1/3) π × 225 × 40.
3. = (1/3) × 9000 π = 3000 π cm³.
4. The cylinder itself holds 9000 π cm³; the cone is one-third of that.
5. So the cone volume is 3000 π cm³.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 8-9 (pp 200-219, 2019 ed.)._
Related questions
Two cones have equal volumes. Their base radii are in the ratio 4 : 5. The ratio of their The volume of a cone with base radius 4 cm and height 6 cm equals:The volume of a cone with base radius r and vertical height h equals:The central angle of the sector required to make a cone with base radius r and slant heighA conical hat is to have base radius 8 cm and slant height 30 cm. Paper area required is aThe curved (lateral) surface area of a cone with base radius r and slant height l is:For a cone of base radius 5 cm and vertical height 10 cm, the slant height is:When a sector of central angle 45° is cut from a circle of radius 12 cm and rolled into a