A rectangular tank whose internal dimensions are 2.4m by 2.5m by 3.7m is two thirds full of juice.

a. Calculate the volume of the juice in liters. (3mks)

b. The juice is parked in small packets in a shape of right pyramid with equilateral triangles of sides 20cm. the height of each packet is 15cm. a full packet is sold at kshs. 50 per packet.

Calculate:

i. The volume of the juice in cm3 of each packet to the nearest whole number. (3mks)

ii. The number of full packets of juice. (2mks)

iii. The amount of money realized from the sale of juice. (2mks)

Let's break down the problem and solve it step by step.

### Part (a): Calculate the volume of the juice in liters.

1. **Calculate the volume of the tank in cubic meters:**

   \[
   \text{Volume of the tank} = \text{length} \times \text{width} \times \text{height} = 2.4 \, \text{m} \times 2.5 \, \text{m} \times 3.7 \, \text{m}
   \]
   \[
   \text{Volume of the tank} = 22.2 \, \text{m}^3
   \]

2. **Since the tank is two-thirds full:**

   \[
   \text{Volume of juice} = \frac{2}{3} \times 22.2 \, \text{m}^3 = 14.8 \, \text{m}^3
   \]

3. **Convert the volume from cubic meters to liters:**

   Since \(1 \, \text{m}^3 = 1000 \, \text{liters}\):

   \[
   \text{Volume of juice} = 14.8 \, \text{m}^3 \times 1000 \, \text{liters/m}^3 = 14800 \, \text{liters}
   \]

So, the volume of the juice is **14,800 liters**.

### Part (b)(i): Calculate the volume of the juice in each packet to the nearest whole number.

The packet is in the shape of a right pyramid with an equilateral triangular base.

1. **Area of the equilateral triangle base:**

   For an equilateral triangle with side length \(s\):
   \[
   \text{Area} = \frac{\sqrt{3}}{4} \times s^2 = \frac{\sqrt{3}}{4} \times (20 \, \text{cm})^2 = \frac{\sqrt{3}}{4} \times 400 \, \text{cm}^2 \approx 173.21 \, \text{cm}^2
   \]

2. **Volume of the pyramid:**

   The volume \(V\) of a pyramid is given by:
   \[
   V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
   \]
   \[
   V = \frac{1}{3} \times 173.21 \, \text{cm}^2 \times 15 \, \text{cm} \approx 866.05 \, \text{cm}^3
   \]

   Rounded to the nearest whole number, the volume of the juice in each packet is **866 cm³**.

### Part (b)(ii): Calculate the number of full packets of juice.

1. **Convert the total volume of juice from liters to cubic centimeters:**

   Since \(1 \, \text{liter} = 1000 \, \text{cm}^3\):

   \[
   \text{Total volume of juice} = 14800 \, \text{liters} \times 1000 \, \text{cm}^3/\text{liter} = 14800000 \, \text{cm}^3
   \]

2. **Calculate the number of packets:**

   \[
   \text{Number of packets} = \frac{14800000 \, \text{cm}^3}{866 \, \text{cm}^3/\text{packet}} \approx 17091
   \]

So, the number of full packets of juice is **17,091**.

### Part (b)(iii): Calculate the amount of money realized from the sale of juice.

1. **Calculate the total revenue:**

   \[
   \text{Total revenue} = 17091 \times 50 \, \text{Kshs} = 854550 \, \text{Kshs}
   \]

So, the amount of money realized from the sale of the juice is **854,550 Kshs**.

---

If you have any questions or need further details, feel free to ask! 

Here are some related questions you might find interesting:
1. How would the calculations change if the tank were only half full?
2. What would happen if the packet shape was cylindrical instead of pyramidal?
3. How would the total revenue change if the price per packet increased by 10%?
4. What is the surface area of one of these juice packets?
5. How many liters of juice would each packet hold?

**Tip:** When dealing with volume conversions, always remember that 1 cubic meter is equivalent to 1000 liters.

Learn how to calculate the volume of juice in a tank and determine revenue from selling packets of juice. Includes step-by-step solutions for converting volume units and calculating pyramid volumes. Suitable for high school level mathematics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation