Advertisements
Advertisements
प्रश्न
Find what length of canvas, 1.5 m in width, is required to make a conical tent 48 m in diameter and 7 m in height. Given that 10% of the canvas is used in folds and stitchings. Also, find the cost of the canvas at the rate of Rs. 24 per metre.
उत्तर
Diameter of the tent = 48 m
Therefore, radius (r) = 24 m
Height (h) = 7 m
Slant height (ℓ) = `sqrt(r^2 + h^2)`
= `sqrt((24)^2 + (7)^2)`
= `sqrt(576 + 49)`
= `sqrt(625)`
= 25 m
Curved surface area = `pirl`
= `22/7xx24xx25`
= `13200/7 m^2`
= 1885.71 m2
But it is given that 10% allowance for folds and stitching
Hence modified area = `1885.71 m^2 + 10/100 xx 1885.71 m^2`
= 2074.28 m2
Width of canvas = 1.5 m
∴ Length of canvas = `"Area of canvas"/"Width of canvas"`
= `(2074.28 m^2)/(1.5 m)`
= 1382.85 m
Now cost of 1 m = Rs. 24
Hence cost of 1382.85 m = Rs. 24 × 1382.85 = Rs. 33188.4.
APPEARS IN
संबंधित प्रश्न
Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.
`["Assume "pi=22/7]`
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 7 cm and area of curved surface is 176 `cm^2`. Find the slant height.
The height of a cone is 21 cm. Find the area of the base if the slant height is 28 cm.
Find the volume of a right circular cone with:
radius 6 cm, height 7 cm.
Find the volume of a right circular cone with:
height 21 cm and slant height 28 cm.
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.
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.
A solid metal sphere is cut through its center into 2 equal parts. If the diameter of the sphere is `3 1/2 cm`, find the total surface area of each part correct to two decimal places.
A solid sphere and a solid hemi-sphere have the same total surface area. Find the ratio between their volumes.
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.
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.
In the following diagram a rectangular platform with a semi-circular end on one side is 22 metres long from one end to the other end. If the length of the half circumference is 11 metres, find the cost of constructing the platform, 1.5 metres high at the rate of Rs. 4 per cubic metres.
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 radius of the circular base of the cone , if its volume is 154 cm3 and the perpendicular height is 12 cm
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 ?
The surface area of a solid sphere is increased by 21% without changing its shape. Find the percentage increase in its: volume
The radius and height of cone are in the ratio 3 : 4. If its volume is 301.44 cm3. What is its radius? What is its slant height? (Take π = 3.14)
A vessel in the form of an inverted cone is filled with water to the brim: Its height is 20 cm and the diameter is 16.8 cm. Two equal solid cones are dropped in it so that they are fully submerged. As a result, one-third of the water in the original cone overflows. What is the volume of each of the solid cones submerged?
