Question

1. a store advertises a circular rug as being 4.9 m². travis wants a rug to fit a rectangular space that is 2.6 m by 2.6 m. will the rug fit?
2. you are designing a rectangular label on a can. the can is 5 cm high, with a diameter of 9 cm. to plan your design, calculate the area of the label. (hint the length of the rectangle will be the diameter of the can)

Explanation:

Problem 2

Step1: Find area of rectangular space

The rectangular space is a square (since both sides are 2.6 m). The area of a rectangle is \( A = l \times w \). So, \( A = 2.6 \times 2.6 \)
\( 2.6 \times 2.6 = 6.76 \, m^2 \)

Step2: Compare areas

The rug's area is \( 4.9 \, m^2 \), and the rectangular space's area is \( 6.76 \, m^2 \). But we need to check if the rug (a circle) can fit in the square. First, find the radius of the circular rug. The area of a circle is \( A = \pi r^2 \), so \( r = \sqrt{\frac{A}{\pi}} \).
\( r = \sqrt{\frac{4.9}{\pi}} \approx \sqrt{\frac{4.9}{3.14}} \approx \sqrt{1.56} \approx 1.25 \, m \). The diameter is \( 2r \approx 2.5 \, m \). The square has sides of 2.6 m. Since the diameter of the rug (≈2.5 m) is less than 2.6 m, the rug will fit.

Step1: Identify dimensions of label

The label is rectangular. The height of the can is the height of the rectangle (\( h = 5 \, cm \)), and the length of the rectangle is the diameter of the can (\( l = 9 \, cm \)).

Step2: Calculate area of rectangle

The area of a rectangle is \( A = l \times h \). So, \( A = 9 \times 5 \)
\( 9 \times 5 = 45 \, cm^2 \)

Answer:

Yes, the rug will fit.

Problem 3