Josie has 260 cubic centimeters of candle wax. She wants to
make a hexagonal prism candle with a base area of 21 square centimeters and a height of 8 centimeters. She also wants to make a triangular prism candle with a height of 14 centimeters. Can the base area of the
triangular prism candle be 7 square centimeters? Explain.
THANK YOU!
To determine if the base area of the triangular prism candle can be 7 square centimeters, we need to compare the volume of the available candle wax with the volume of both candles.
First, let's calculate the volume of the hexagonal prism candle using the formula:
Volume = Base Area * Height
The base area of the hexagonal prism candle is given as 21 square centimeters, and the height is 8 centimeters. Therefore, the volume of the hexagonal prism candle can be found as:
Volume1 = 21 cm² * 8 cm
Volume1 = 168 cm³
Next, let's calculate the volume of the triangular prism candle. However, we have an unknown base area for this candle. So, let's consider the formula for the volume of a triangular prism:
Volume = (1/2) * Base Area * Height
Here, we know that the height of the triangular prism candle is 14 centimeters, and we are given that the base area might be 7 square centimeters. Thus, the volume of the triangular prism candle can be calculated as:
Volume2 = (1/2) * 7 cm² * 14 cm
Volume2 = 49 cm³
Now, we can check if the given amount of 260 cubic centimeters of candle wax is sufficient to create both candles. The total volume of the candles should be less than or equal to 260 cm³.
Total Volume = Volume1 + Volume2
Total Volume = 168 cm³ + 49 cm³
Total Volume = 217 cm³
Since the total volume of the two candles is 217 cubic centimeters, which is less than the available amount of candle wax (260 cubic centimeters), it is indeed possible for the base area of the triangular prism candle to be 7 square centimeters.
Therefore, it is valid for Josie to make a triangular prism candle with a base area of 7 square centimeters.
The hexagonal prism candle requires 21 x 8 = 168cc of wax.
After that, 260 - 168 = 92cc of wax would remain.
A triangular prism candle with a height of 14 centimeters and a base area of 7 square centimeters would require 14 x 7 = 98cc of wax, which is more than she has remaining.