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A right triangle, whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of π as found appropriate.)

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Short Answer Type

442.

A cistern, internally measuring 150 cm × 120 cm × 110 cm, has 129600 cm³ of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each brick being 22.5 cm × 7.5 cm × 6.5 cm?

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443.

In one fortnight of a given month, there was a rainfall of 10 cm in a river valley. If the area of the valley is 7280 km2, show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each 1072 km long, 75 m wide and 3 m deep.

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444.

An oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel (see the given Fig.

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Long Answer Type

445.

Derive the formula for the curved surface area and total surface area of the frustum of a cone, given to you in Section 13.5, using the symbols as explained.

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Short Answer Type

446.

Derive the formula for the volume of the frustum of a cone, given to you in Section 13.5, using the symbols as explained.

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447. The radius and height of a cylinder are in the ratio 5:7 and its volume is 550 cm³. Find its radius.

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448. The curved surface area of height circular cone is 12320 cm². If the radius of the base is 56 cm, find its height.

Here, we have r = 56 cm
and, Curved Surface Area = 12320

$rightwards double arrow space space 22 over 7 space straight x space 56 space straight x italic space straight l space equals space 12320 rightwards double arrow space space l space equals space 70 space cm Now comma Height space left parenthesis straight h right parenthesis space equals space square root of l to the power of italic 2 minus straight r squared end root equals space square root of open parentheses 70 close parentheses squared minus left parenthesis 56 right parenthesis squared end root equals space square root of 4900 minus 3136 end root equals square root of 1764 equals space 42 space space space$
Hence, height of one cone = 42 cm.

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449. A conical flask is full of mater. The flask was base m radius r and height n. the mater is poored into a cylindrical flask of base radius mr. find the height of water in the cylindrical flask.

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