Question

Find the dimensions of a cuboid with volume of 2py^2+6py-20p

Answer 1

Volume of a cuboid

=length X Breadth X height


volume of cuboid = 2py^2 + 6py - 20p

= 2py^2 + 10py - 4py - 20p

= 2py(y+5) - 4p(y+5)

= (2py-4p) (y+5)

= 2p(y-2)(y+5)


then the dimensions of cuboid

= (2p) , (y-2) , (y+5)

Answer 2

Concept:

Three Dimensional Geometry

Volume of a cuboid is given by,

V = lbh

where V = Volume of the cuboid

l = Length of the cuboid

b = Breadth of the cuboid

h = Height of the cuboid

Given:

Volume of a cuboid is (2py² + 6py - 20p).

Find:

The dimensions of the cuboid.

Answer:

The dimensions of the cuboid are 2p, (y + 5) and (y - 2).

Solution:

Volume of the cuboid, V = (2py² + 6py - 20p)

But V = lbh

∴ lbh = (2py² + 6py - 20p)

l×b×h = (2py² + 6py - 20p)

l×b×h = 2p (y² + 3y - 10)

l×b×h = 2p (y² + 5y - 2y - 10)

l×b×h = 2p [y(y + 5) -2(y + 5)]

l×b×h = 2p (y + 5) (y - 2)

l×b×h = (2p) × (y + 5) × (y - 2)

Comparing both sides, we get

l = 2p

b = (y + 5)

h = (y - 2)

Hence, the dimensions of the cuboid are 2p, (y + 5) and (y - 2) respectively.

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