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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.

Let r cm be the radius and h cm be the height of the cone, then
r = 2 cm, h = 8 cm
Let r₁ cm be the radius of the sphere.
Since, sphere is made out of the cone, so their volumes are equal.
Therefore,

$1 third πr squared straight h space equals 4 over 3 πr subscript 1 cubed rightwards double arrow space straight r squared straight h space space equals space 4 straight r subscript 1 cubed rightwards double arrow space straight r subscript 1 cubed equals 1 fourth straight r squared straight h rightwards double arrow space straight r subscript 1 cubed equals 1 fourth straight x space 2 space straight x space 2 space straight x space 8 rightwards double arrow space straight r subscript 1 cubed equals space 2 space straight x space 2 space straight x space 2 rightwards double arrow space straight r subscript 1 equals space 2 space cm$

Hence, diameter of sphere = 4 cm.

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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.

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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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