English

Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r cm.

Advertisements
Advertisements

Question

Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r cm. 

Sum
Advertisements

Solution

 
For the volume of cone to be largest, h = r cm

Volume of the cone 

= `1/3pir^2h` 

= `1/3pi xx r^2 xx r` 

= `1/3pir^3`  

shaalaa.com
  Is there an error in this question or solution?
Chapter 20: Cylinder, Cone and Sphere - Exercise 20 (E) [Page 312]

APPEARS IN

Selina Concise Mathematics [English] Class 10 ICSE
Chapter 20 Cylinder, Cone and Sphere
Exercise 20 (E) | Q 7. | Page 312

RELATED QUESTIONS

Find the surface area of a sphere of radius 5.6 cm.


A hollow sphere of internal and external diameter 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone. 


The total area of a solid metallic sphere is 1256 cm2. It is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate :

  1. the radius of the solid sphere.
  2. the number of cones recast. [Take π = 3.14]

A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones.


The cross-section of a tunnel is a square of side 7 m surmounted by a semi-circle as shown in the adjoining figure. The tunnel is 80 m long.

Calculate:

  1. its volume,
  2. the surface area of the tunnel (excluding the floor) and
  3. its floor area.   


Find the total surface area of a hemisphere of radius 10 cm.


The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is 


A sphere has the same curved surface area as the curved surface area of a cone of height 36 cm and base radius 15 cm . Find the radius of the sphere . 


A vessel is in he form of an inverted cone. Its height is 11 cm., and the radius of its top which is open is 2.5 cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.25 cm., are dropped 2 into the vessel, `2/5`th of the water flows out. Find the number of lead shots dropped into the vessel.


The internal and external diameters of a hollow hemispherical vessel are 20 cm and 28 cm respectively. Find the cost to paint the vessel all over at ₹ 0.14 per cm2


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×