To find the volume of a right rectangular pyramid, you can use the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
where the base area for a rectangle is given by:
\[ \text{Base Area} = \text{Length} \times \text{Width} \]
Step 1: Calculate the volume of the first pyramid
Given:
- Length = 26 m
- Width = 31 m
- Height = 35 m
Calculate Base Area:
\[ \text{Base Area} = 26 \times 31 = 806 , \text{m}^2 \]
Calculate Volume:
\[ V = \frac{1}{3} \times 806 \times 35 \]
\[ V = \frac{1}{3} \times 28210 = 9403.33 , \text{m}^3 \]
Step 2: Calculate the volume of the pyramid at the Louvre Museum
Given:
- Base side length = 112 ft (this is a square pyramid)
- Height = 71 ft
Calculate Base Area:
\[ \text{Base Area} = 112 \times 112 = 12544 , \text{ft}^2 \]
Calculate Volume:
\[ V = \frac{1}{3} \times 12544 \times 71 \]
\[ V = \frac{1}{3} \times 890144 = 296714.67 , \text{ft}^3 \]
Step 3: Calculate the volume of the new juice bottle
Given:
- Base dimensions = 8 cm by 15 cm
- Height = 22 cm
Calculate Base Area:
\[ \text{Base Area} = 8 \times 15 = 120 , \text{cm}^2 \]
Calculate Volume:
\[ V = \frac{1}{3} \times 120 \times 22 \]
\[ V = \frac{1}{3} \times 2640 = 880 , \text{cm}^3 \]
Summary of Volumes
- Volume of the first pyramid: 9403.33 m³
- Volume of the Louvre pyramid: 296714.67 ft³
- Volume of the new juice bottle: 880 cm³