The spires on the roof of a cathedral shown below are made of solid concrete. Select the formula you need and use it to determine how much more concrete is required to build the la... The spires on the roof of a cathedral shown below are made of solid concrete. Select the formula you need and use it to determine how much more concrete is required to build the larger spire. Read more

Steps to Solve

1. Calculate the volume of the larger spire

Given that the larger spire has a base area $B_1 = 28 \text{ ft}^2$ and a height $h_1 = 12 \text{ ft}$, we can calculate its volume $V_1$ using the formula $V = \frac{1}{3}Bh$: $$ V_1 = \frac{1}{3} \times B_1 \times h_1 = \frac{1}{3} \times 28 \text{ ft}^2 \times 12 \text{ ft} $$ $$ V_1 = \frac{1}{3} \times 336 \text{ ft}^3 = 112 \text{ ft}^3 $$

2. Calculate the volume of the smaller spire

The smaller spire has a base area $B_2 = 24 \text{ ft}^2$ and a height $h_2 = 10 \text{ ft}$. Therefore, its volume $V_2$ is: $$ V_2 = \frac{1}{3} \times B_2 \times h_2 = \frac{1}{3} \times 24 \text{ ft}^2 \times 10 \text{ ft} $$ $$ V_2 = \frac{1}{3} \times 240 \text{ ft}^3 = 80 \text{ ft}^3 $$

3. Find the difference in volume

To find how much more concrete is required for the larger spire, we subtract the volume of the smaller spire from the volume of the larger spire: $$ \text{Difference} = V_1 - V_2 = 112 \text{ ft}^3 - 80 \text{ ft}^3 = 32 \text{ ft}^3 $$