Advertisements
Advertisements
प्रश्न
Find the volume of the right circular cone whose height is 12 cm and slant length is 15 cm . (π = 3.14)
उत्तर
Slant length = l = 15 cm
Height = h = 12 cm
Radius of the base = r
We know ,
`l^2 = h^2 + r^2`
⇒ `r^2 = l^2 - h^2`
⇒ r = `sqrt(l^2 - h^2)`
⇒ r = `sqrt(15^2 - 12^2)`
⇒ r = 9 cm
Radius = 9 cm
Volume = `1/3 xx (pir^2) xx h`
= `1/3 xx 3.14 xx 9 xx 9 xx 12`
= 1017.36 cm3
Volume of the cone = 1017.36 cm3
APPEARS IN
संबंधित प्रश्न
The following figure represents a solid consisting of a right circular cylinder with a hemisphere at one end and a cone at the other. This common radius is 7 cm. The height of the cylinder and cone are each of 4 cm. Find the volume of the solid.
Find the curved surface area of a cone with base radius 5.25 cm and slant height 10cm.
The radius and the height of a right circular cone are in the ratio 5 : 12. If its volume is 314 cubic meter, find the slant height and the radius (Use it 𝜋 = 3.14).
A cylinder and a cone have equal radii of their bases and equal heights. Show that their volumes are in the ratio 3:1.
Find the volume of the largest right circular cone that can be fitted in a cube whose edge is 14 cm.
The volume of a right circular cone is 9856 cm3. If the diameter of the base is 28 cm, find:
(i) height of the cone (ii) slant height of the cone (iii) curved surface area of the cone.
Monica has a piece of Canvas whose area is 551 m2. She uses it to have a conical tent made, with a base radius of 7m. Assuming that all the stitching margins and wastage incurred while cutting, amounts to approximately 1 m2. Find the volume of the tent that can be made with it.
The circumference of the base of a 12 m high conical tent is 66 m. Find the volume of the air contained in it.
Two right circular cone x and y are made x having three times the radius of y and y having half the volume of x. Calculate the ratio between the heights of x and y.
The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cone of height 32 cm. Find the diameter of the base of the cone.
The horizontal cross-section of a water tank is in the shape of a rectangle with semi-circle at one end, as shown in the following figure. The water is 2.4 metres deep in the tank. Calculate the volume of water in the tank in gallons.
A solid is in the form of a right circular cone mounted on a hemisphere. The diameter of the base of the cone, which exactly coincides with hemisphere, is 7 cm and its height is 8 cm. The solid is placed in a cylindrical vessel of internal radius 7 cm and height 10 cm. How much water, in cm3, will be required to fill the vessel completely?
Curved surface area of a cone is 251.2 cm2 and radius of its base is 8 cm. Find its slant height and perpendicular height. (π = 3.14)
What will be the cost of making a closed cone of tin sheet having radius of base 6 m and slant height 8 m if the rate of making is Rs.10 per sq.m? `(π = 22/7)`
Total surface area of a cone is 616 sq.cm. If the slant height of the cone is three times the radius of its base, find its slant height.
Find the radius of the circular base of the cone , if its volume is 154 cm3 and the perpendicular height is 12 cm
The volume of a conical tent is 1232 m3 and the area of the base floor is 154 m2. Calculate the: height of the tent.
The surface area of a solid sphere is increased by 21% without changing its shape. Find the percentage increase in its: volume
