Advertisements
Advertisements
Question
A heap of wheat is in the form of a cone of diameter 16.8 m and height 3.5 m. Find its volume. How much cloth is required to just cover the heap?
Solution
Diameter of the cone = 16.8 m
Therefore, radius (r) = 8.4 m
Height (h) = 3.5 m
i. Volume of heap of wheat = `1/3pir^2h`
= `1/3 xx 22/7 xx (8.4)^2 xx 3.5`
= `1/3 xx 22/7 xx 8.4 xx 8.4 xx 3.5`
= 258.72 m3
ii. Slant height (l) = `sqrt(r^2 + h^2)`
`sqrt((8.4)^2 + (3.5)^2)`
= `sqrt(70.56 + 12.25)`
= `sqrt(82.81)`
= 9.1 m
Therefore, cloth required or curved surface area = πrℓ
= `22/7 xx 8.4 xx 9.1`
= 240.24 m2
APPEARS IN
RELATED QUESTIONS
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 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.
Find the total surface area of a right circular cone with radius 6 cm and height 8 cm.
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.
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.
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.
Find the volume of a right circular cone with:
radius 6 cm, height 7 cm.
The radius and the height of a right circular cone are in the ratio 5 : 12. If its volume is 314 cubic meter, find the slant height and the radius (Use it 𝜋 = 3.14).
Find the volume of the largest right circular cone that can be fitted in a cube whose edge is 14 cm.
There are two cones. The curved surface area of one is twice that of the other. The slant height of the latter is twice that of the former. Find the ratio of their radii.
A solid cone of height 8 cm and base radius 6 cm is melted and recast into identical cones, each of height 2 cm and diameter 1 cm. Find the number of cones formed.
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 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 given figure shows the cross section of a water channel consisting of a rectangle and a semi-circle. Assuming that the channel is always full, find the volume of water discharged through it in one minute if water is flowing at the rate of 20 cm per second. Give your answer in cubic metres correct to one place of decimal.
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 given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm and the other dimensions are as shown. Calculate: the total volume of the solid.
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)
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)
Water flows at the rate of 10 m per minute through a cylindrical pipe 5 mm of diameter. How much time would it take to fill a conical vessel whose diameter at he surface is 40 cm and depth is 24 cm?
