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Surface Areas and Volumes

Short Answer Type

541. An iron pole consisting of a cylindrical portion 110 cm high and base diameter 12cm is surmounted by a cone 9cm high. Find the mass of the pole it is given that 1cm³of iron has 8 gm mass.

open parentheses bold Use bold space bold pi bold space bold equals bold space bold 355 over bold 113 close parentheses

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Long Answer Type

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.

Let R and r be respectively the radii of bigger and smaller ends of the frustum
Then, R = 20 cm and r = 8 cm
Let h and l be the height and slant height of frustum, then
h = 16

$and space space space space space space space l italic space equals space square root of straight h squared plus left parenthesis straight R minus straight r right parenthesis squared end root space space space space space space space space space space space space space space equals space square root of left parenthesis 16 right parenthesis squared plus left parenthesis 20 minus 8 right parenthesis squared end root space space space space space space space space space space space space space space equals space square root of 256 plus 144 end root space space space space space space space space space space space space space space equals space square root of 400 equals 20 space cm$
Now,
Curved surface area of the frustum
$equals space πl space left parenthesis straight R plus straight r right parenthesis equals space 22 over 7 straight x 20 space left parenthesis 20 plus 8 right parenthesis equals space 22 over 7 space straight x space 20 space straight x space 28 equals space 1760 space cm squared$
Total metal sheet required
= C. S. A. + Area of base

$equals space 1760 space plus space 22 over 7 space straight x space 8 space straight x space 8$
= 1760 + 201.14
= 1961.14 cm²
Cost of metal sheet used

$equals space 1961.14 space straight x space 15 over 100$

= Rs 294.17

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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?

449 Views

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.

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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.

1458 Views