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Surface Areas and Volumes

Short Answer Type

471. Three equal cubes of side 4 cm are joined end to end. Find the surface area of the resulting cuboid.

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472.

Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm are melted and a new cube is made (i) Find the length of the edge of the new cube.
(ii) Find the total surface area of the new cube.

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473. Two cubes each of 12 cm edge are joined end to end. Find the surface area of the resulting cuboid.

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474. A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.

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475. A right circular cone is 8 cm heigh and the radius of its base is 2 cm. The cone is melted and re-cast into a sphere. Determine the diameter of the sphere.

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476. A solid cylinder of metal 8 m high and 4 m diameter is melted and recast into a cone of diameter 3 m. Find the height of the cone.

Let h cm be the height and r cm be the radius of a cylinder, then
h = 8 m
and r =

4 over 2 space equals space 2 space m

Let r₁ m be the radius and m be the height of the cone, then

straight r subscript 1 equals 3 over 2 equals 1.5 space straight m comma straight h subscript 1 equals ?

Since a cone is made out of the solid cylinder, so their volumes are equal.
Therefore,
$rightwards double arrow space space space πr squared straight h space equals space 1 third πr subscript 1 squared straight h subscript 1 rightwards double arrow space space space 2 space straight x space 2 space straight x space 8 space equals space 1 third straight x space 1.5 space straight x space 1.5 space straight x space straight h subscript 1 rightwards double arrow space space space straight h subscript 1 equals fraction numerator 2 space straight x space 2 space straight x space 8 space straight x space 3 over denominator 1.5 space straight x space 1.5 end fraction space space space space space space space space space space space equals space fraction numerator 96 over denominator 2.25 end fraction equals 42.66 space straight m$

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477. A cone is 8.4 cm high and the radius of its base is 2.1 cm. it is melted and recast into a sphere. Find the radius of the sphere.

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478. A well of diameter 14 m is dug 15 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 7 m to form an embankment. Find the height of the embankment.

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479. An agriculture field is in the form of a rectangle of length 20 m, and width 14 m. A 10 m deep well of diameter 7 m is dug in a comer of the field and the earth taken out of the well is spread evenly over the remaining part of the field. Find the rise in the level of the field.

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480. A metallic sphere of radius 10.5 cm is melted and recast into 5 small cones each of radius 3.5 cm and height 3 cm. Find how many cones are obtained.

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