Advertisements
Advertisements
Question
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.
Solution
Let radius of first cone be 3r and height be h, then radius of second cone will be rand height will be 3h.
Volume of cone = `1/3 xx (pir^2) xx h`
Ratio of volumes of cone = `"Volume of first cone"/"Volume of second cone"`
= `(1/3 xx (pi(3r)^2) xx h)/(1/3 xx (pir^2) xx 3h)`
= `(1/3 pi9r^2h)/(1/3pir^2 3h)`
= `3/1`
Ratio of volumes of cone = 3:1
APPEARS IN
RELATED QUESTIONS
A conical tent is 10 m high and the radius of its base is 24 m. Find
- slant height of the tent.
- cost of the canvas required to make the tent, if the cost of 1 m2 canvas is ₹ 70.
`["Assume "pi=22/7]`
A joker’s cap is in the form of right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.
`["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.
A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the cone.
A circus tent is cylindrical to a height of 3 meters and conical above it. If its diameter is 105 m and the slant height of the conical portion is 53 m, calculate the length of the canvas 5 m
wide to make the required tent.
A bus stop is barricated from the remaining part of the road, by using 50 hollow cones made of recycled card-board. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs. 12 per m2, what will be the cost of painting all these cones. (Use 𝜋 = 3.14 and √1.04 = 1.02)
Find the volume of a right circular cone with:
radius 3.5 cm, height 12 cm
Two cones have their heights in the ratio 1 : 3 and the radii of their bases in the ratio 3 : 1. Find the ratio of their volumes.
A right angled triangle of which the sides containing he right angle are 6.3 cm and lo cm in length, is made to turn round on the longer side. Find the volume of the solid, thus generated. Also, find its curved surface area.
A heap of wheat is in the form of a cone of diameter 16.8 m and height 3.5 m. Find its volume. How much cloth is required to just cover the heap?
The volume of a conical tent is 1232 m3 and the area of the base floor is 154 m2. Calculate the:
- radius of the floor,
- height of the tent,
- length of the canvas required to cover this conical tent if its width is 2 m.
A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. Find the number of spheres formed.
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.
From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm and depth 24 cm is drilled out. Find :
- the surface area of remaining solid,
- the volume of remaining solid,
- the weight of the material drilled out if it weighs 7 gm per cm3.
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?
The curved surface area of a right circular cone of radius 11.3 cm is 710 cm2. What is the slant height of the cone ?
A buoy is made in the form of a hemisphere surmounted by a right circular cone whose circular base coincides with the plane surface of the hemisphere. The radius of the base of the cone is 3.5 m and its volume is two-third the volume of hemisphere. Calculate the height of the cone and the surface area of the buoy, correct to two decimal places.
The internal and external diameters of a hollow hemi-spherical vessel are 21 cm and 28 cm respectively. Find: total 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.
