Advertisements
Advertisements
Question
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.
Solution
Let the radius of base and slant height of the cone be r cm and l cm, respectively.
Slant height of the cone = 3 × Radius of the cone ...(Given)
∴ l = 3r
Total surface area of the cone = 616 cm2
∴ πr (r + l) = 616 cm2
⇒ `22/7 xx r xx (r + 3r)` = 616
⇒ `22/7 xx r xx 4r` = 616
⇒ `88/7` r2 = 616
⇒ r2 = ` [616 xx 7]/88`
⇒ r2 = 49
⇒ r = `sqrt 49` = 7cm
∴ Slant height of the cone, l = 3r = 3 × 7 = 21 cm
Thus, the slant height of the cone is 21 cm.
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]`
Find the ratio of the curved surface areas of two cones if their diameters of the bases are equal and slant heights are in the ratio 4 : 3.
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 Rs. 210 per l00 m2.
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.
The area of the base of a conical solid is 38.5 cm2 and its volume is 154 cm3. Find the curved surface area of the solid.
The internal and external diameter of a hollow hemispherical vessel are 21 cm and 28 cm respectively. Find :
- internal curved surface area,
- external curved surface area,
- total surface area,
- volume of material of the vessel.
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 vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm, are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
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 circumference of the base of a 10 m high conical tent is 44 metres. Calculate the length of canvas used in making the tent if the width of the canvas is 2m. (Take π = 22/7)
