Question

alistair has a cube - shaped box that... what is the edge length of alistair’s...

1. what is the formula for the volume... l x w x h
2. if you know the volume of a cube, edge length? $sqrt3{216}=l$
3. how would you write the edge length... cube root? $sqrt3{216}=l$
4. fill in the boxes to find the cube root...

$sqrt3{216}=sqrt3{6cdot\boxed{6}cdot\boxed{6}}$
$=sqrt3{\boxed{6}^3}$
$=\boxed{6}$

1. what is the edge length of alistair’s... 6 in
2. sian’s room is in the shape of a squ... how long is one side of sian’s room... one side is 11ft long

Explanation:

For Question 4:

Step 1: Factorize 216

We know that \(216 = 6\times6\times6\), so we fill the first two boxes with 6 and 6 (since \(6\times6\times6 = 216\)).
\(\sqrt[3]{216}=\sqrt[3]{6\cdot6\cdot6}\)

Step 2: Recognize the cube form

Since \(6\times6\times6 = 6^{3}\), we fill the next box with 6 (because \(6\cdot6\cdot6=6^{3}\)).
\(=\sqrt[3]{6^{3}}\)

Step 3: Simplify the cube root

The cube root of a number cubed is the number itself, so \(\sqrt[3]{6^{3}} = 6\), and we fill the last box with 6.
\(= 6\)

For Question 5:

Step 1: Recall the volume formula for a cube

The volume \(V\) of a cube with edge length \(s\) is \(V=s^{3}\). To find the edge length \(s\) when we know the volume, we take the cube root of the volume, i.e., \(s = \sqrt[3]{V}\).

Step 2: Apply the formula

From the previous steps, we found that \(\sqrt[3]{216}=6\). Assuming the volume of Alistair's cube - shaped box is 216 cubic units (from the cube - root calculation \(\sqrt[3]{216}\)), the edge length \(s=\sqrt[3]{216} = 6\) units (in the answer, it's given as 6 in, so we assume the unit is inches).

For Question 6 (assuming the area of the square - shaped room is 121 square feet, since the answer is 11 ft long, as \(11\times11 = 121\)):

Step 1: Recall the area formula for a square

The area \(A\) of a square with side length \(s\) is \(A = s^{2}\). To find the side length \(s\) when we know the area, we take the square root of the area, i.e., \(s=\sqrt{A}\).

Step 2: Apply the formula

If we assume the area \(A = 121\) square feet (since \(11\times11=121\)), then \(s=\sqrt{121}=11\) feet.

Answer:

s:

• Question 4: The filled boxes are (from top to bottom, left to right) \(6\), \(6\), \(6\), \(6\).
• Question 5: The edge length of Alistair's box is \(\boldsymbol{6}\) inches.
• Question 6: One side of Sian's room is \(\boldsymbol{11}\) feet long.