# A rectangular shed is 3m long, 2m wide, and 2m high. If each dimension is increased by the same amount, the volume is doubled. How do you find to the nearest tenth of a meter the amount by which each dimension is increased?

Jul 1, 2016

I found $0.6 m$

#### Explanation:

The original volume will be:
$V = 3 \cdot 2 \cdot 2 = 12 {m}^{3}$
let call the increase (the same for each dimension) $x$ so we get:
$V ' = \left(3 + x\right) \left(2 + x\right) \left(2 + x\right) = 2 V = 24 {m}^{3}$
So:
$\left(3 + x\right) \left(4 + 4 x + {x}^{2}\right) = 24$
$12 + 12 x + 3 {x}^{2} + 4 x + 4 {x}^{2} + {x}^{3} = 24$
${x}^{3} + 7 {x}^{2} + 16 x - 12 = 0$

Let us plot it (having this possibility!!!):

graph{x^3+7x^2+16x-12 [-10, 10, -5, 5]}

So that by inspecting the graph I get $x = 0.6 m$