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551. A container (open at the top) made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find
(i) the cost of milk when it is completely filled with milk at the rate of Rs. 15 per litre.
(ii) the cost of metal sheet used, if it costs Rs. 5 per 100 cm². (Take π = 3.14)

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552. An open container made up of a metal sheet is in the form of a frustum of a cone of height 8 cm with radii of its lower and upper ends as 4 cm and 10 cm respectively.
Find the cost of oil which can completely fill the container at the rate of Rs. 50 per litre. Also, find the cost of metal used, if it costs Rs. 5 per 100 cm² (Use π = 3.14).

1376 Views

553.

A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm respectively. Find the volume of the bucket. Also find the cost of the bucket if the cost of metal sheet used is Rs. 20 per 100 cm². (Use $straight pi$ = 3.14)

6202 Views

Short Answer Type

554. From a solid cylinder whose height is 8 cm and radius 6 cm, a conical cavity of height 8 cm and of base radius 6 cm, is hollowed out. Find the volume of the remaining solid correct to two places of decimals. Also find the total surface area of the remaining solid.
(Take π = 3.1416).

2086 Views

Long Answer Type

555.

A cylindrical vessel, with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the volume of
(i) Water displaced out of the cylinderical vessel,
(ii) Water left in the cylindrical vessel.

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

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556. A bucket is in the form of a frustum of a cone with a capacity of 12308.8 cm³. The radii of the top and bottom circular ends of the bucket are 20 cm and 12 cm respectively. Find the height of the bucket and also the area of metal sheet used in making it. (Use $straight pi$ = 3.14)

Radius of frustum,
r = 12 cm, R = 20 cm, V = 12308.8 cm³.

Radius of frustum,r = 12 cm, R = 20 cm, V = 12308.8 cm3.

$straight V subscript frustrum equals 1 third πh left parenthesis left parenthesis straight R squared plus straight r squared plus Rr 123088 over 10 equals 1 third straight x 314 over 100 straight x space straight h left parenthesis 400 plus 144 plus 240 right parenthesis 123088 over 10 equals 314 over 100 xhx 784 over 3 straight h space equals space 15 space cm straight l space equals space square root of 225 plus 64 end root equals square root of 289 equals 17 space cm. area left parenthesis metal space sheet space used right parenthesis space equals space straight pi left parenthesis straight R plus straight r right parenthesis straight l plus πr squared equals straight pi left parenthesis 32 space straight x space 17 right parenthesis space plus straight pi left parenthesis 144 right parenthesis equals straight pi left parenthesis 544 space plus space 144 right parenthesis equals space 314 over 100 left parenthesis 688 right parenthesis space equals space 216032 over 100 equals space 2160.32 space cm squared space$

4737 Views

Short Answer Type

557. A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. If the total height of the toy is 15.5 cm. Find the total surface area.

open parentheses bold Use bold space bold pi bold space bold equals bold space bold 22 over bold 7 close parentheses

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558. A circus tent is cylindrical to a height of 3 m and conical above it. If its base radius is 52 m and slant height of the conical portion is 53 m, find the area of the canvas needed to make the tent.

open parentheses bold Use bold space bold pi bold space bold equals bold space bold 22 over bold 7 close parentheses

70 Views

559. A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 25 cm. Find the total surface area of the vessel.

open parentheses bold Use bold space bold pi bold space bold equals bold space bold 22 over bold 7 close parentheses

131 Views

560. An iron pole consisting of a cylindrical portions 110 cm high and of base diameter 12 cm is surmounted by a cone 9 cm high. Find the total surface area of the pole.