Question
Pause now and try the next problem. What is the Volume of the pyramid?
B= 1/2 (3) (5)=7.5
V= 1/3 (7.5) (6)=
15cm
180 in3
90 in3
56 in3
280 in3
B= 1/2 (3) (5)=7.5
V= 1/3 (7.5) (6)=
15cm
180 in3
90 in3
56 in3
280 in3
Answers
Answered by
GPT-4o mini
Let's break down the calculation for the volume of the pyramid step by step.
1. **Calculate the Base Area (B)**:
The area of the base (B) is given by the formula for the area of a triangle:
\[
B = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 3 \times 5 = \frac{15}{2} = 7.5 \text{ cm}^2
\]
2. **Calculate the Volume (V)**:
The volume (V) of the pyramid can be calculated using the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height} = \frac{1}{3} \times 7.5 \times 6 = \frac{45}{3} = 15 \text{ cm}^3
\]
The volume of the pyramid is 15 cm³.
Now, looking at the options provided (180 in³, 90 in³, 56 in³, 280 in³), none of the options match the volume we calculated for the pyramid, which is 15 cm³. It seems like there might be a confusion between cubic centimeters (cm³) and cubic inches (in³).
If you need a conversion from cm³ to in³, keep in mind that:
1 cm³ ≈ 0.0610237 in³
However, since the calculations here yield 15 cm³ directly, none of the provided options are correct for the volume obtained. Would you like more assistance or clarification?
1. **Calculate the Base Area (B)**:
The area of the base (B) is given by the formula for the area of a triangle:
\[
B = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 3 \times 5 = \frac{15}{2} = 7.5 \text{ cm}^2
\]
2. **Calculate the Volume (V)**:
The volume (V) of the pyramid can be calculated using the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height} = \frac{1}{3} \times 7.5 \times 6 = \frac{45}{3} = 15 \text{ cm}^3
\]
The volume of the pyramid is 15 cm³.
Now, looking at the options provided (180 in³, 90 in³, 56 in³, 280 in³), none of the options match the volume we calculated for the pyramid, which is 15 cm³. It seems like there might be a confusion between cubic centimeters (cm³) and cubic inches (in³).
If you need a conversion from cm³ to in³, keep in mind that:
1 cm³ ≈ 0.0610237 in³
However, since the calculations here yield 15 cm³ directly, none of the provided options are correct for the volume obtained. Would you like more assistance or clarification?