Advertisements
Advertisements
प्रश्न
A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8:5, show that the radius of each is to the height of each as 3:4.
उत्तर
Let us assume radius of cone=r.
Also, radius of cylinder=r.
And, height of cylinder=h.
Let` C_1` , be the curved surface area of cone
`∴ C_1=pirsqrt(r^2+h^2)`
Similarly,` C_2` be the curved surface area of cone cylinder.
`∴ C_2=2pirh`
According to question `C_2/C_1=8/5`
⇒ `(2pirh)/(pirsqrt(r^2+h^2))=8/5`
⇒ `10h=8sqrt(r^2+h^2)`
⇒ `100h^2=64r^2+64h^2`
⇒ `36h^2=64r^2`
`h/r=sqrt64/30`
⇒`(h/r)^2=64/36`
⇒` b/r=sqrt64/30=8/6=4/3`
`∴ r/h=3/4`
APPEARS IN
संबंधित प्रश्न
Find the curved surface area of a cone with base radius 5.25 cm and slant height 10cm.
If the radius of the base of a cone is halved, keeping the height same, what is the ratio of the volume of the reduced cone to that of the original cone?
Find the volume of the largest right circular cone that can be fitted in a cube whose edge is 14 cm.
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 radius and the height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the radius and slant height of the cone. (Take π = 3.14)
A vessel, in the form of an inverted cone, is filled with water to the brim. Its height is 32 cm and diameter of the base is 25.2 cm. Six equal solid cones are dropped in it, so that they are fully submerged. As a result, one-fourth of water in the original cone overflows. What is the volume of each of the solid cones submerged?
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 cone of height 15 cm and diameter 7 cm is mounted on a hemisphere of same diameter. Determine the volume of the solid thus formed.
The ratio of the radii of two right circular cones of the same height is 1 : 3. Find the ratio of their curved surface area when the height cone is 3 times the radius of the smaller cone.
A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5 m. How many students can sit in the tent if a student, on an average, occupies `5/7` m2 on the ground?
