CAPACITY As a gift, you fill the calendar with packets of chocolate candy. Each packet has a volume of 2 cubic inches. Find the maximum number of CALENDAR 6 in. packets you can fit inside the calendar. Answer: 8 in. 4 in.
CAPACITY As a gift, you fill the calendar with packets of chocolate candy. Each packet has a volume of 2 cubic inches. Find the maximum number of CALENDAR 6 in. packets you can fit inside the calendar. Answer: 8 in. 4 in.
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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![**Capacity Problem**
**Question:**
As a gift, you fill the calendar with packets of chocolate candy. Each packet has a volume of 2 cubic inches. Find the maximum number of packets you can fit inside the calendar.
**Image Explanation:**
The image depicts a desk calendar with dimensions labeled. The calendar has a triangular prism shape with a base length of 8 inches, a height of 6 inches, and a triangular depth of 4 inches.
**Steps to Solve:**
1. **Calculate the Volume of the Calendar:**
- The calendar forms a triangular prism.
- The area of the triangular base can be calculated using the formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{base length} \times \text{height}
\]
- Here, the base length is 8 inches and the height is 6 inches:
\[
\text{Area} = \frac{1}{2} \times 8 \times 6 = 24 \text{ square inches}
\]
- The volume of the prism is the area of the triangular base multiplied by the depth (4 inches):
\[
\text{Volume} = \text{Area} \times \text{depth} = 24 \times 4 = 96 \text{ cubic inches}
\]
2. **Calculate the Number of Packets:**
- Each packet has a volume of 2 cubic inches.
- To find the maximum number of packets, divide the volume of the calendar by the volume of one packet:
\[
\frac{\text{Volume of Calendar}}{\text{Volume of One Packet}} = \frac{96}{2} = 48
\]
**Answer:**
48 packets can fit inside the calendar.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87804e42-439c-4b15-9fec-573b7a02348d%2Fabf0d297-c0b1-49be-b9c1-0e1b0c6e09c1%2Fz2o7amj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Capacity Problem**
**Question:**
As a gift, you fill the calendar with packets of chocolate candy. Each packet has a volume of 2 cubic inches. Find the maximum number of packets you can fit inside the calendar.
**Image Explanation:**
The image depicts a desk calendar with dimensions labeled. The calendar has a triangular prism shape with a base length of 8 inches, a height of 6 inches, and a triangular depth of 4 inches.
**Steps to Solve:**
1. **Calculate the Volume of the Calendar:**
- The calendar forms a triangular prism.
- The area of the triangular base can be calculated using the formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{base length} \times \text{height}
\]
- Here, the base length is 8 inches and the height is 6 inches:
\[
\text{Area} = \frac{1}{2} \times 8 \times 6 = 24 \text{ square inches}
\]
- The volume of the prism is the area of the triangular base multiplied by the depth (4 inches):
\[
\text{Volume} = \text{Area} \times \text{depth} = 24 \times 4 = 96 \text{ cubic inches}
\]
2. **Calculate the Number of Packets:**
- Each packet has a volume of 2 cubic inches.
- To find the maximum number of packets, divide the volume of the calendar by the volume of one packet:
\[
\frac{\text{Volume of Calendar}}{\text{Volume of One Packet}} = \frac{96}{2} = 48
\]
**Answer:**
48 packets can fit inside the calendar.
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