Find the surface area and volume of a rectangular pyramid of length = 5 units, width = 4 units, and height = 7 units
A rectangular pyramid is a three-dimensional object with a rectangle for a base and a triangular face corresponding to each side of the base.
Answer: For a rectangular pyramid of length = 5 units, width = 4 units, and height = 7 units, the Surface area is 86.132 square units and the volume is 46.666 cubic units.
Surface area is defined as the total area that the surface occupies totally and volume is defined as the amount of space that is filled in the particular container.
Explanation:
Surface area of rectangular pyramid = area of base + 1/2 × perimeter of base × slant height
= l × w + l √ {(w/2)2 + h2} + w √{(l/2)2 + h2}
Length = 5 units, width = 4 units, height = 7 units
Surface area = 5 × 4 + 5 √ {(4/2)2 + 72} + 4 √{(5/2)2 + 72}
= 20 + 5 √ {(2)2 + 72} + 4 √{(2.5)2 + 72}
= 20 + 5 √ (4 + 49) + 4 √(6.25 + 49)
= 20 + 5 √ (53) + 4 √(55.25)
= 20 + 5(7.280) + 4(7.433)
= 20 + 36.4 + 29.732
= 86.132 square units.
Volume of rectangular pyramid = (l × w × h)/3
Volume = (5 × 4 × 7)/3
= 140/3
= 46.666 cubic units.
Therefore, the surface area is 86.132 square units and the volume is 46.666 cubic units.
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