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 total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.
`["Assume "pi=22/7]`
A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. 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 ₹ 12 per m2, what will be the cost of painting all these cones?
`("Use "π = 3.14" and take "sqrt1.04= 1.02)`
The radius of a cone is 5 cm and vertical height is 12 cm. Find the area of the curved surface.
Find the curved surface area of a cone with base radius 5.25 cm and slant height 10cm.
A cubical block of side 7 cm is surmounted by a hemisphere of the largest size. Find the surface area of the resulting solid.
A solid metallic hemisphere of diameter 28 cm is melted and recast into a number of identical solid cones, each of diameter 14 cm and height 8 cm. Find the number of cones so formed.
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.
The curved surface area of a cone is 2200 sq.cm and its slant height is 50 cm. Find the total surface area of cone. `(π = 22/7)`
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.
A hollow metallic cylindrical tube has an internal radius of 3.5 cm and height 21 cm. The thickness of the metal tube is 0.5 cm. The tube is melted and cast into a right circular cone of height 7 cm. Find the radius of the cone, correct to one decimal place.
