Question

Find the ratio of the surface area to volume of the rectangular prism brlow

Answer 1

`A = 2(width*length) + 2(length*height)+2(width*height)\\=> 2(wl+lh+wh)\\where \ w = width,\  l=length \ and \ h = height`

l = 8, w = 5, h = 6

A = 2(5*8 + 8*6 + 5*6)

A = 236

`Volume = width * length * height\\V = wlh`

V = 5*8*6

V = 240

Ratio of A to V = A / V

236/240 = 236:240

Explanation:

The surface area of any object is the total area of each face of that object. Now, we have a rectangular prism with dimensions given. Considering a face of the prism, there is an opposite face and this is why the area of each face was multiplied by 2. That is how the formula for the surface area of an object is derived

For the volume, the formula is multiplying the height, width and length

When the area and volume is computed, we now take the ratio of the answers to arrive at 236/240 which in ratio form is 236:240