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542. A tent is in the form of a cylinder surmounted by a conical top. If the height and diameter of the cylinderical part are 2.1 m and 4m respectively, and the height of the top is 2.8m, find the area of the canvas used for making the tent. Find the cost of the canvas used for making the tent. Find the cost of the canvas of the tent at the rate of Rs. 500 per m². Also, find the volume of air enclosed in the tent.

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543. A toy is in the form of a cone mounted on a hemisphere with same radius. The diameter of the base of the conical portion is 7.0 cm and the total height of the toy is 14.5 cm. Find

the volume of the toy

open square brackets Use space straight pi space equals space 22 over 7 close square brackets.

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544. An iron pillar has lower part in the form of a right circular cylinder and the upper part in the form of a right circular cone. The radius of the base of each of the cone and cylinder is 8 cm. The cylindrical part is 240 cm high and the conical part is 36 cm high. Find the weight of the pillar if 1 cm³ of iron weighs 7.5 grams.

open parentheses Take space straight pi space equals space 22 over 7 close parentheses

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Short Answer Type

545. A bucket is made up of a metal sheet is in the form of a frustum of a cone of height 16cm with radii of its lower and upper ends at 8cm and 20cm respectively. Find the cost of the bucket, if the cost of metal sheet used is Rs. 15 per 100 cm².

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Long Answer Type

546. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be

1 over 27

of the volume of the given cone, at which height above the base is the section made?

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547. A hollow cone is cut by a plane parallel to the base and the upper portul is removed. If the curved surface of the remainder is

8 over 9

of the curved surface of the whole cone, find the ratio of the line-segment into which the cones altitude is divided by the plane.

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548. If the radii of the circular ends of a conical bucket, which is 16 cm high, are 20 cm and 8 cm, find the capacity and total surface area of the bucket.

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549. A bucket is in the form of a frustum of a cone and holds 28.49 litres of milk. The radii of the top and bottom are 28 cm and 21 cm. Find the height of the bucket.

Let ‘R’ be the radius ‘r’ be the bottom of the frustum of cone. Then,
R = 28 cm, r = 21 cm.
let ‘h’ cm be the height of the frustum of a cone.
Now,
Volume of frustum of cone = (28.49 x 1000) cm³
$equals space 1 third πrh space left parenthesis straight R squared plus straight r squared plus Rr right parenthesis space equals space 28490 equals space 1 third space straight x space 22 over 7 space straight x space straight h space left square bracket left parenthesis 28 right parenthesis squared plus left parenthesis 21 right parenthesis squared space plus space 28 space straight x space 21 right parenthesis right square bracket space equals space 28490 equals space 1 third space straight x space 22 over 7 space straight x space straight h space left square bracket 784 plus 441 plus 588 right square bracket space equals space 28490 equals space 1 third space straight x space 22 over 7 space straight x space straight h space left square bracket space 1813 space right square bracket space equals space 28490 equals space straight h space equals space fraction numerator 28490 space straight x space 3 space straight x space 7 over denominator 22 space straight x space 1813 end fraction space equals space 15 space cm space$

Hence, Height of bucket = 15 cm.

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Short Answer Type

550.

A bucket of height 8 cm made up of copper sheets is in the form of frustum of a right circular cone with radii of its lower ends as 3 cm and 9 cm respectively. Calculate
(i) the height of the cone of which the bucket is a part.
(ii) the volume of water which can be filled in the bucket.
(iii) the area of copper sheet required to make the bucket.

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