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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.

Let the length, breadth and height of the cuboid be l, b and h units respectively. Then, p = lb q = bh r = hl
∴ pqr = (lb)(bh)(hl) = l²b²h² ...(1) Again, v = Ibh
∴ v² = (Ibh)² = l²b²h² ...(2)
(1) and (2) give
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.

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129. Find the length of the longest rod that can be placed in a room 12 m x 9 m x 8 m.

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130. If v is the volume of a cuboid of dimensions a, b and c and s is its surface area, then prove that

1 over straight v equals 2 over straight s open parentheses 1 over straight b plus 1 over straight b plus 1 over straight c close parentheses

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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

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

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