Advertisements
Advertisements
Question
The volume of a conical tent is 1232 m3 and the area of the base floor is 154 m2. Calculate the: length of the canvas required to cover this conical tent if its width is 2 m.
Solution
Let l be the slant height of the conical tent, then
`= l=sqrt(h^2+r^2)`
∴ `l= sqrt(h^2+r^2)=sqrt((24)^2+(7)^2)=sqrt(576+49)=sqrt625=25m`
The area of the canvas required to make the tent =`pirlm^2`
∴`pirl=22/7xx7xx25m^2=550m^2`
Length of the canvas required to cover the conical tent of its width 2 m= `550/2=275 m`
APPEARS IN
RELATED QUESTIONS
What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm. [Use π = 3.14]
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]`
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]`
Find the curved surface area of a cone with base radius 5.25 cm and slant height 10cm.
The area of the curved surface of a cone is 60 cm2. If the slant height of the cone be 8 cm, find the radius of the base?
Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find the radius of the base and total surface area of the cone.
Find the volume of a right circular cone with:
height 21 cm and slant height 28 cm.
The ratio of volumes of two cones is 4 : 5 and the ratio of the radii of their bases is 2:3. Find the ratio of their vertical heights.
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.
The curved surface area of a cone is 12320 cm2. If the radius of its base is 56 cm, find its height.
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 if it is completely filled.
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.
The cross-section of a railway tunnel is a rectangle 6 m broad and 8 m high surmounted by a semi-circle as shown in the figure. The tunnel is 35 m long. Find the cost of plastering the internal surface of the tunnel (excluding the floor) at the rate of Rs. 2.25 per m2.
A solid, consisting of a right circular cone standing one a hemisphere, is placed upright in a right circular cylinder, full of water, and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of
the hemisphere is 2 cm and the height of cone is 4 cm. Give your answer to the nearest cubic centimeter.
Volume of a cone is 1232 cm3 and its height is 24 cm. Find the surface area of the cone. `( π = 22/7)`
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.
Find the curved surface area of a cone whose height is 8 cm and base diameter is 12 cm .
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.
The volume of a conical tent is 1232 m3 and the area of the base floor is 154 m2. Calculate the: height of the tent.
The internal and external diameters of a hollow hemi-spherical vessel are 21 cm and 28 cm respectively. Find: total surface area.
