Question

The diagram shows a square prism with cross-secon x units by x units, and length (9-2x) units
What is the maximum volume of the prism?
1) 16 units
2) 24 units
3) 27 units
(
4) 30 units​

Answer 1

Explanation:

27 all dirty fellows who wrote wrong

Answer 2

The correct answer is option 3.

Given: Dimensions of square prism = x units, x units and (9-2x) units.

To Find: Maximum volume of the prism.

Solution:

Square prism means the shape is cuboidal.

So, the volume of cuboid(V) is lbh.

lbh = (x)(x)(9 - 2x)

V = lbh = $9x^{2} -2x^{3}$

As we have to find maximum volume. Differentiate with respect to x, make the equation equal to 0 and find the value of x.

$\frac{dV}{dx} =18x-6x^{2}$

$\frac{dV}{dx}$ = 0   (Make the derivative equal to zero)

$18x-6x^{2}$ = 0

x (18 - 6x) = 0

x = 0 and 3.

But we will not take 0 as it will make volume 0 and we want maximum volume.

So x = 3.

Volume = $9(3)^{2}-2(3)^{3}$

= 27 units

Hence, the maximum volume is 27 units.

#SPJ3