Question

suppose the height of a pyramid with a square base is decreased by p% and the lengths of the sides of its square base are increased by p% where p>0 if the volume remains the same then

Answer 1

Step-by-step explanation:

Let the length of base be x and height be y

Volume of pyramid =

3

1

×l×b×h

When height is decreased by p%, then h=y−

100

p

×y

And base is increased, b=x+

100

p

×x

Volume in both cases is same

3

1

x

2

y=

3

1

x

2

(1+

100

p

)

2

×y(1−

100

p

)

⇒p

2

+100p−100

2

=0

solving the equation by using quadratic formula

p=±

12500

−50

p can't be negative

∴p=

12500

−50

⇒p≃61.80