Question

the dimensions of a triangular pyramid are shown in the diagram.14 ft10 ft12 ftwhat is the volume of the triangular pyramid in cubic feet?the dimensions of a triangular pyramid are shown in the diagram. the volume of the pyramid is 864 cubic meters.h24 m18 mwhat is the height of the triangular pyramid in meters?a handmade chocolate treat in the shape of a rectangular pyramid has a height of 10 centimeters. the area of the base of the chocolate treat is 45 square centimeters.what is the volume of the handmade chocolate treat in cubic centimeters?a scented candle is in the shape of a square pyramid with a height of 6 inches.the dimensions of a square pyramid are shown in the diagram.a puzzle is in the triangular pyramid 14 cm. the

Explanation:

Step1: Calculate base area (tri. pyramid 1)

Base area: $\frac{1}{2} \times 12 \times 10 = 60$ sq. ft

Step2: Compute volume (tri. pyramid 1)

Volume: $\frac{1}{3} \times 60 \times 14 = 280$ cubic ft
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Step1: Calculate base area (tri. pyramid 2)

Base area: $\frac{1}{2} \times 18 \times 24 = 216$ sq. m

Step2: Solve for height $h$

Rearrange volume formula: $h = \frac{3V}{\text{base area}} = \frac{3 \times 864}{216} = 12$ m
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Step1: Compute volume (rect. chocolate treat)

Volume: $\frac{1}{3} \times 45 \times 10 = 150$ cubic cm

Answer:

1. Volume of the first triangular pyramid: 280 cubic feet
2. Height of the second triangular pyramid: 12 meters
3. Volume of the chocolate treat: 150 cubic centimeters