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

Solution

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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Probability

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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A table cover 4 m x 2 m is spread on a table. Find the cost of polishing the top of the table at र40 per square metre of 25 cm table cover is hanging all round the table.

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Two cubes of side 6 cm each, are joined end to end. Find the surface area of the resulting cuboid.

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For Daily Free Study Material Join wiredfaculty

Probability

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

Some More Questions From Probability Chapter

A table cover 4 m x 2 m is spread on a table. Find the cost of polishing the top of the table at र40 per square metre of 25 cm table cover is hanging all round the table.

A classroom is 7 m long, 6.5 m wide and 4 m high. It has one door 3 m x 1.4 m and three windows each measuring 2 m x 1 m. The interior wall is to be colour washed. Find the cost of colour washing at the rate of र 3.50 per m2.

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The length, breadth and height of a cuboid are 15 cm, 10 cm and 20 cm. Find the surface area of the cuboid.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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