Question

1. a sprinkler sprays water 1.5 m as it rotates. what is the area of the lawn that is sprinkled? show your work.
2. corrine is painting a plate that has a length of 35 cm from the centre.

a) what is the area of the plate?
b) if one bottle of paint can cover $0.15\\ \text{m}^2$, how many bottles will she need to paint 3 layers?

1. find the area of the figure below. round to the nearest tenth cm.

Explanation:

(Problem 4):

Step1: Identify radius, use circle area formula

The sprinkler's spray distance is the radius $r=1.5$ m. The area of a full circle is $A=\pi r^2$.

Step2: Calculate the sprinkled area

$$A=\pi \times (1.5)^2 = 2.25\pi \approx 7.07$$

(Problem 5a):

Step1: Identify radius, convert to meters (optional)

The plate's radius $r=35$ cm $=0.35$ m. Use circle area formula $A=\pi r^2$.

Step2: Calculate the plate area

$$A=\pi \times (0.35)^2 = 0.1225\pi \approx 0.385$$
In square centimeters: $A=\pi \times 35^2 = 1225\pi \approx 3848.45$

(Problem 5b):

Step1: Calculate total area for 3 layers

Total area $= 3 \times 0.385 = 1.155$ m²

Step2: Divide by coverage per bottle

Number of bottles $=\frac{1.155}{0.15}=7.7$; round up to whole bottles.

(Problem 6):

Step1: Identify figure dimensions

The figure is a semicircle with diameter $d=6$ cm, so radius $r=3$ cm. Area of a semicircle is $A=\frac{1}{2}\pi r^2$.

Step2: Calculate the semicircle area

$$A=\frac{1}{2} \times \pi \times 3^2 = 4.5\pi \approx 14.1$$

Answer:

(Problem 4):
$\approx 7.07$ square meters

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