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प्रश्न
An oil funnel of the tin sheet consists of a cylindrical portion 10 cm long attached to a frustum of a cone. If the total height is 22 cm, the diameter of the cylindrical portion by 8 cm and the diameter of the top of the funnel be 18 cm, then find the area of the tin sheet required to make the funnel.
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उत्तर
Total height of oil funnel = 22 cm
Height of the cylindrical portion = 10 cm
Height of the frustum (h) = 22 – 10 = 12 cm
Radius of the cylindrical portion = 4 cm
Radius of the bottom of the frustum = 4 cm
Top radius of the funnel (frustum) = `18/2` = 9 cm
Area of the tin sheet required = C.S.A of the frustum + C.S.A of the cylinder
= π (R + r) l + 2πrh sq.units.
= `[pi(9 + 4) sqrt(12^2 + (9 - 4)^2) + 2pi xx 4 xx 10]"cm"^2`
= `pi[13 xx sqrt(144 + 25) + 25 + 80]"cm"^2`
= `22/7 [13 xx 13 + 80] "cm"^2`
= `22/7 [169 + 80] "cm"^2`
= `22/7 xx 249 "cm"^2`
= 782.57 cm2
Area of sheet required to make the funnel = 782.57 cm2
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संबंधित प्रश्न
Derive the formula for the curved surface area and total surface area of the frustum of cone.
A 5 m wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used at the rate of Rs 25 per metre ?\[[Use \pi = \frac{22}{7}]\]
A bucket, made of metal sheet, is in the form of a cone whose height is 35 cm and radii of circular ends are 30 cm and 12 cm. How many litres of milk it contains if it is full to the brim? If the milk is sold at Rs 40 per litre, find the amount received by the person.
A frustum of a cone is 9 cm thick and the diameters of its circular ends are 28 cm and 4 cm. Find the volume and lateral surface area of the frustum.
(Take π = 22/7).
A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 16 cm and 12 cm. Find the capacity of the glass.
A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter `"4"2/3` cm and height 3 cm. Find the number of cones so formed.
The volume of the frustum of a cone is `1/3 pih[r_1^2 + r_2^2 - r_1r_2]`, where h is vertical height of the frustum and r1, r2 are the radii of the ends.
The curved surface area of a frustum of a cone is πl (r1 + r2), where `l = sqrt(h^2 + (r_1 + r_2)^2)`, r1 and r2 are the radii of the two ends of the frustum and h is the vertical height.
Find the total surface area of frustum, if its radii are 15 cm and 7 cm. Also, the slant height of the frustum is 14 cm.
Radii of the frustum = `square` cm and `square` cm
Slant height of the frustum = `square` cm
Total surface area = `π[(r_1^2 + r_2^2 + (r_1 + r_2)l]`
= `22/7 [square + square + (square + square) square]`
= `22/7 (square)`
= `square` cm2
Hence, the total surface area of the frustum is `square`.
Find the curved surface area of a right circular cone whose height is 15 cm and base radius is 8 cm. tan β = `3/4`.
