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Surface Areas and Volumes

Short Answer Type

481. Find the number of coins 1.5 cm in diameter and 0.2 cm thick to be melted to form a right circular cylinder whose height is 8 cm and diameter 6 cm.

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482. Spherical marbles of diameter 1.4 cm each are dropped in a cylindrical beaker of radius 3.5 cm containing some water. Find the number of marbles that should be dropped into the beaker so that the water level in the beaker rises by 5.6 cm.

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483. The radius of a conical solid is melted and recaste into a number of cylindrical solids if the radius of the cone is three times the radius of the cylinder and the height of the cone is four times the height of the cylinder, find the number of cylindrical solids.

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484. Water flows at the rate of 10 m per minute through a cylindrical pipe having its diameter as 5 mm. How much time will it take to fill a conical vessel whose diameter of the base is 40 cm and depth 24 cm.

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485. Water is flowing at the rate of 0.70 m/sec through a circular pipe, whose internal diameter is 2 cm into a cylindrical tank the radius of whose base is 40 cm. Determine the increase in the water level in 1/2 hour.

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486. Water in a canal 30 dm wide and 12 dm deep, is flowing velocity of 10 km/hr. How much area will it irrigate if 8 cm of standing water is required for irrigation?

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487. A hemispherical tank full of water is emptied by a pipe at the rate of litres per second. How much time will it take to half empty the tank, if the tank is 3 m in diameter.

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488. Water is flowing at the rate of 5 km per hour through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Determine the time in which the level of water in the tank will rise by 7 cm.

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489. Water is flowing at the rate of 3 km/ hr through a circular pipe of 20 cm external diameter into a circular cistern of diameter 10m and depth 2 m. In how much time will the cistern be filled.

Let R cm be the radius and H cm be the height of a circular pipe, then

straight R space equals space 20 over 2 space equals space 10 space cm space equals space 1 over 10 space straight m

H (depth) = 3 km = 3000 m.
Now, Volume of water that flows out of the circular pipe in 1 hour = πR²H

$equals space open parentheses straight pi space straight x space 1 over 10 straight x 1 over 10 straight x 3000 close parentheses space straight m cubed equals space 30 straight pi space straight m cubed$
Let r m be the radius and h m be the depth (height) of a circular cistern, then

$straight r space equals space 10 over 2 equals 5 space straight m space and space straight h space equals space 2 space straight m$

Now, Volume of water that flows in the circular cistern
= π r²h
= π x 5 x 5 x 2 = 50 π m³.
Hence,
Time taken to fill up the cistern

$equals space space space space space space space space space space space space space Volume space of space water space that space flows space space space space space fraction numerator out space the space circular space pipe space in space 1 space hr over denominator Volume space of space water space that space flows space in space the space cistem end fraction equals fraction numerator 50 straight pi over denominator 30 straight pi end fraction equals fraction numerator 5 straight pi over denominator 3 straight pi end fraction equals space 5 over 2 equals 1 space hour space 40 space minutes$

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490. An iron solid sphere of radius 3 cm is melted and recast into small spherical balls of radius 1 cm each. Assuming that there is no wastage in the process, find the number of small spherical balls made from the given sphere.

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