https://file.aiquickdraw.com/mathbot/file/1721685388752ckprtgr3.png

Franklin wants to work out how much weed killer he needs for his flower beds. 30ml of weed killer will cover 20m2 of land. He has 40 flower beds of this size.

How much weed killer will he need to the nearest 10ml?

To determine how much weed killer Franklin needs, we first need to calculate the area of one flower bed.

The flower bed has a length of 5 meters and a width of 90 cm (0.9 meters). Since the ends are semicircles, we can calculate the area in two parts: the rectangular part and the two semicircular ends.

1. **Rectangular Part:**
   \[
   \text{Area of the rectangle} = \text{length} \times \text{width} = 5 \, \text{m} \times 0.9 \, \text{m} = 4.5 \, \text{m}^2
   \]

2. **Semicircular Ends:**
   The diameter of each semicircle is equal to the width of the rectangle, which is 0.9 meters. The radius \( r \) is half of the diameter:
   \[
   r = \frac{0.9}{2} = 0.45 \, \text{m}
   \]
   The area of one circle is given by \( \pi r^2 \). Since we have two semicircles, their combined area is equal to the area of one full circle:
   \[
   \text{Area of the circles} = \pi \times (0.45)^2 = 0.2025 \pi \, \text{m}^2
   \]
   Approximating \(\pi \) as 3.14:
   \[
   \text{Area of the circles} \approx 0.2025 \times 3.14 = 0.636 \, \text{m}^2
   \]

3. **Total Area of One Flower Bed:**
   \[
   \text{Total area} = \text{Area of the rectangle} + \text{Area of the circles} = 4.5 \, \text{m}^2 + 0.636 \, \text{m}^2 = 5.136 \, \text{m}^2
   \]

Now, Franklin has 40 flower beds of this size:
\[
\text{Total area} = 40 \times 5.136 \, \text{m}^2 = 205.44 \, \text{m}^2
\]

Next, we determine the amount of weed killer needed. Since 30 ml of weed killer covers 20 m²:
\[
\text{Amount of weed killer needed} = \frac{30 \, \text{ml}}{20 \, \text{m}^2} \times 205.44 \, \text{m}^2
\]
\[
\text{Amount of weed killer needed} = 30 \times \frac{205.44}{20} \approx 30 \times 10.272 = 308.16 \, \text{ml}
\]

Rounding to the nearest 10 ml:
\[
\text{Amount of weed killer needed} \approx 310 \, \text{ml}
\]

Franklin will need approximately **310 ml** of weed killer.

Would you like further details or have any questions?

Here are some questions you might find helpful:
1. How do you calculate the area of a circle?
2. How do you convert square meters to square centimeters?
3. What is the formula for the circumference of a circle?
4. How do you calculate the volume of a cylinder?
5. What is the relationship between milliliters and liters?

**Tip:** Remember to always double-check your units when performing area and volume calculations to ensure accuracy.

Learn how to calculate the amount of weed killer needed for Franklin's flower beds with a step-by-step guide. This problem involves calculating the area of flower beds, converting units, and applying the ratio of weed killer to area covered. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation