Karen is making a cake with two layers. For the bottom layer, she uses a large cylindrical cake pan. The pan has a radius of 6 inches and a height of 2 inches. What is the volume o... Karen is making a cake with two layers. For the bottom layer, she uses a large cylindrical cake pan. The pan has a radius of 6 inches and a height of 2 inches. What is the volume of the cake pan? Use π ≈ 3.14 and round your answer to the nearest whole number. For the top layer, she uses a smaller cylindrical cake pan. It has the same height, but a radius of 3 inches. What is the volume of the smaller cake pan? Use π ≈ 3.14 and round your answer to the nearest whole number. What is the total volume of the cake pans? Round your answer to the nearest whole number.
Understand the Problem
The question asks to find the volume of two cylindrical cake pans and then the combined total volume. We will use the formula for the volume of a cylinder, which is (V = \pi r^2 h), where (r) is the radius and (h) is the height. The value of (\pi) is given as approximately 3.14. We need to calculate the volume of the larger pan, the smaller pan, and then add those two volumes together.
Answer
226 cubic inches 57 cubic inches 283 cubic inches
Answer for screen readers
226 cubic inches 57 cubic inches 283 cubic inches
Steps to Solve
-
Calculate the volume of the larger cake pan. The larger pan has a radius (r = 6) inches and a height (h = 2) inches. Use the formula (V = \pi r^2 h) with (\pi \approx 3.14). $$V_{large} = 3.14 \cdot (6^2) \cdot 2$$ $$V_{large} = 3.14 \cdot 36 \cdot 2$$ $$V_{large} = 3.14 \cdot 72$$ $$V_{large} = 226.08$$ Rounding to the nearest whole number, the volume of the larger pan is 226 cubic inches.
-
Calculate the volume of the smaller cake pan. The smaller pan has a radius (r = 3) inches and a height (h = 2) inches. Use the formula (V = \pi r^2 h) with (\pi \approx 3.14). $$V_{small} = 3.14 \cdot (3^2) \cdot 2$$ $$V_{small} = 3.14 \cdot 9 \cdot 2$$ $$V_{small} = 3.14 \cdot 18$$ $$V_{small} = 56.52$$ Rounding to the nearest whole number, the volume of the smaller pan is 57 cubic inches.
-
Calculate the total volume of the cake pans. Add the volumes of the larger and smaller pans. $$V_{total} = V_{large} + V_{small}$$ $$V_{total} = 226.08 + 56.52$$ $$V_{total} = 282.6$$
Rounding to the nearest whole number, the total volume is 283 cubic inches.
226 cubic inches 57 cubic inches 283 cubic inches
More Information
The volumes represent how much batter each cake pan can hold, and the total volume represents the combined batter needed for both cake layers.
Tips
A common mistake is forgetting to square the radius in the volume formula. Another mistake is not rounding the answers to the nearest whole number as requested in the problem.
AI-generated content may contain errors. Please verify critical information
