Advertisements
Advertisements
प्रश्न
A cone and a hemisphere have the same base and the same height. Find the ratio between their volumes.
उत्तर
Let the radius of base be 'r' and the height be 'h'
Volume of cone, `V_c`
= `1/3pir^2h`
Volume of hemisphere, `V_h`
= `2/3pir^3`
`V_c/V_h = (1/3pir^2r)/(2/3pir^3)`
`=> V_c/V_h = 1/2`
APPEARS IN
संबंधित प्रश्न
Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find
- radius of the base and
- total surface area of the cone.
`["Assume "pi =22/7]`
The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of ₹ 210 per 100 m2.
`["Assume "pi=22/7]`
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 total surface area of a right circular cone with radius 6 cm and height 8 cm.
Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.
The curved surface area of a cone is 4070 cm2 and its diameter is 70 cm. What is its slant height? (Use it 𝜋 = 22/7).
A heap of wheat is in the form of a cone of diameter 9 m and height 3.5 m. Find its volume. How much canvas cloth is required to just cover the heap? (Use 𝜋 = 3.14).
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.
A solid metallic cone, with radius 6 cm and height 10 cm, is made of some heavy metal A. In order to reduce its weight, a conical hole is made in the cone as shown and it is completely filled with a lighter metal B. The conical hole has a diameter of 6 cm and depth 4 cm. Calculate the ratio of the volume of metal A to the volume of the metal B in the solid.
A buoy is made in the form of hemisphere surmounted by a right cone whose circular base coincides with the plane surface of hemisphere. The radius of the base of the cone is 3.5 metres and its volume is two-third of the hemisphere. Calculate the height of the cone and the surface area of the buoy, correct to two places of decimal.
The radii of the bases of two solid right circular cones of same height are r1 and r2 respectively. The cones are melted and recast into a solid sphere of radius R. Find the height of each cone in terms r1, r2 and R.
In the following diagram a rectangular platform with a semi-circular end on one side is 22 metres long from one end to the other end. If the length of the half circumference is 11 metres, find the cost of constructing the platform, 1.5 metres high at the rate of Rs. 4 per cubic metres.
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)`
Find the volume of the right circular cone whose height is 12 cm and slant length is 15 cm . (π = 3.14)
The heights of two cones are in the ratio 1:3 and their base radii are in the ratio 3:1. Find the ratio of their volumes.
The total surface area of a right circular cone of slant height 13 cm is 90π cm2. Calculate: its volume in cm3. Take π = 3.14
The internal and external diameters of a hollow hemi-spherical vessel are 21 cm and 28 cm respectively. Find: external curved surface area .
The given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm and the other dimensions are as shown. Calculate: the total volume of the solid.
How many square metres of canvas is required for a conical tent whose height is 3.5 m and the radius of the base is 12 m?
