A sculpture is made of solid brass in the shape of a cone. The sculpture is 90 inches tall, and its base has a radius of 6 inches. If brass costs $0.55 per cubic inch, how much did the brass for the sculpture cost? Use 3.14 for n, and do not round your answer.
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.
![### Volume of Prisms and Cylinders
**Question:**
A sculpture is made of solid brass in the shape of a cone. The sculpture is 90 inches tall, and its base has a radius of 6 inches. If brass costs $0.55 per cubic inch, how much did the brass for the sculpture cost?
Use \( \pi = 3.14 \) for \( \pi \), and do not round your answer.
**Answer:**
- **Height (h)**: 90 inches
- **Radius (r)**: 6 inches
- **Cost per cubic inch**: $0.55
The volume \( V \) of a cone can be calculated using the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
Substitute the given values into the formula:
\[ V = \frac{1}{3} \times 3.14 \times (6)^2 \times 90 \]
Calculate the volume:
\[ V = \frac{1}{3} \times 3.14 \times 36 \times 90 \]
\[ V = \frac{1}{3} \times 3.14 \times 3240 \]
\[ V = \frac{1}{3} \times 10183.2 \]
\[ V = 3394.4 \, \text{cubic inches} \]
Cost of the brass = Volume \( \times \) Cost per cubic inch
\[ \text{Cost} = 3394.4 \times 0.55 \]
\[ \text{Cost} = 1866.92 \, \text{dollars} \]
### Explanation
The problem requires calculating the volume of a cone-shaped sculpture and then finding out the cost based on the volume and the price per cubic inch of the material used. The key steps involve using the geometric formula for the volume of a cone and then converting that volume into a monetary cost using simple multiplication.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd8d11063-2bda-4ec0-87e2-714d5471412b%2F36290684-8524-46cf-8033-72778c95f3fd%2F6w5ojqr_processed.jpeg&w=3840&q=75)
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