Question

The given graph shows the radius of the cakes Hannah baked for her bakery and the total quantity of the ingredients she used.


If Hannah has to bake an $8$-inch-wide cake, what will the total quantity of the ingredients (in lb) that she will need be?

• A. $12$ Ib
• B. $10$ Ib
• C. $15$ Ib
• D. $14$ Ib

Answer 1

The correct option is A $12$ Ib

First, let’s tabulate the points given on the graph.

$x$	$y$
$1$	$3$
$2$	$6$
$3$	$9$

Now, we can connect the points in the graph and observe the line passing through the origin.


This means the graph has a unit rate $r$ and the point $(1,r)$ lies on the line.
When $x=1,y=3$
Therefore, $r=3$

Total quantity of ingredients needed to bake a cake of radius 1 in = $3$ lb

We need to find the quantity of ingredients needed to bake an $8$-inch-wide cake.
This means the diameter of the cake is $8$ in.

Therefore, radius of the cake will be $\frac{8}{2}=4$ in

Total quantity of ingredients needed to bake a cake of radius
$4$ in =$(3\times 4)=12$ lb