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Capacity of the box = [25 – (2 + 2)} x [18 – (2 + 2)} x {15 – (2 + 2)} = 21 x 14 x 11 cm 3 = 3234 cm 3 Volume of the wood used = 25 x 18 x 15 cm 3 – 3234 cm 3 = 6750 cm 3 – 3234 cm 3 = 3516 cm 3

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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.

Capacity of the box
= [25 – (2 + 2)} x [18 – (2 + 2)} x {15 – (2 + 2)} = 21 x 14 x 11 cm³ = 3234 cm³Volume of the wood used
= 25 x 18 x 15 cm³ – 3234 cm³= 6750 cm³ – 3234 cm³ = 3516 cm³

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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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