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Surface Areas and Volumes

Short Answer Type

121.

A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?

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122. An underground water tank is in the form of a cuboid of edges 48 m, 36 m and 28 m. Find the volume of the tank.

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123. The areas of three adjacent faces of a cuboid are p, q and r. If its volume is v, prove that v² = pqr.

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124. Three cubes of edge 12 cm are joined together (end to end). Find the volume of the resulting cuboid.

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125. A box with lid is made out of 2 cm thick wood. Its external length, breadth and height are 25 cm, 18 cm and 15 cm respectively. Find the capacity of the box and volume of the wood used.

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126. A rectangular metallic sheet has dimensions 48 cm x 36 cm. From each of its comers, a square of side 8 cm is cut off and an open box is made from the remaining sheet, find the volume of the box.

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127.

A cubical box has each edge of length 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high. Find the volume of the box which has greater lateral surface area.

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128. The total surface area of a cube isExample 3. The total surface area of a cube is $32 2 over 3$ Find the volume of the cube.

Let the length of each edge of the cube be a m.

Total surface area of the cube = $32 2 over 3 space straight m cubed$

$rightwards double arrow space space space space space space space space 6 straight s squared equals 98 over 3 rightwards double arrow space space space space space space space space space straight a squared equals fraction numerator 98 over denominator 3 cross times 6 end fraction rightwards double arrow space space space space space space space space space straight a squared equals 49 over 9 rightwards double arrow space space space space space space space space space straight a space equals space square root of 49 over 9 end root rightwards double arrow space space space space space space space space space straight a equals 7 over 3 space straight m$
$therefore$ Volumen of the cube = a³
$equals open parentheses 7 over 3 close parentheses cubed equals 343 over 27 space straight m cubed$ .