At her local market, Joanna purchases a regular-size can of tomato paste. The cylindrical can has a radius of 2 cm and a height of 5 cm. At the warehouse club, she sees a value-size can of tomato paste that contains 4 times as much tomato paste as the regular size. Which of these could be the dimensions of the cylindrical value-size can? radius = 8 cm, height = 20 cm B.O radius = 4 cm, height = 10 cm c.O radius = 4 cm, height = 5 cm D. radius = 16 cm, height = 5 cm
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![**Problem Description:**
At her local market, Joanna purchases a regular-size can of tomato paste. The cylindrical can has a radius of 2 cm and a height of 5 cm. At the warehouse club, she sees a value-size can of tomato paste that contains 4 times as much tomato paste as the regular size. Which of these could be the dimensions of the cylindrical value-size can?
**Answer Choices:**
A. radius = 8 cm, height = 20 cm
B. radius = 4 cm, height = 10 cm
C. radius = 4 cm, height = 5 cm
D. radius = 16 cm, height = 5 cm
### Explanation and Solution:
To determine which of these dimensions could be the value-size can, we need to compare their volumes relative to the regular-size can.
**Step-by-Step Solution:**
1. **Calculate the volume of the regular-size can:**
The volume of a cylinder is given by the formula:
\[
V = \pi r^2 h
\]
For the regular-size can:
\[
r = 2 \, \text{cm}, \quad h = 5 \, \text{cm}
\]
Substitute the values into the formula:
\[
V = \pi (2)^2 (5) = 20\pi \, \text{cm}^3
\]
2. **Determine the volume of the value-size can:**
The value-size can contains 4 times as much tomato paste as the regular-size can. Thus, its volume is:
\[
4 \times 20\pi = 80\pi \, \text{cm}^3
\]
3. **Check each answer choice by calculating the volume:**
- **Option A: radius = 8 cm, height = 20 cm**
\[
V = \pi (8)^2 (20) = 1280\pi \, \text{cm}^3 \quad \text{(not equal to } 80\pi \text{)}
\]
- **Option B: radius = 4 cm, height = 10 cm**
\[
V = \pi (4)^2 (10) = 160\pi \, \text{cm}^3 \quad \text](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb602927-d5c2-4b17-99bc-cf43c066f5a5%2Ffe44dd51-5c6a-462f-848d-d71d3822745e%2Fltnugee_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 6 images
