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The base of a pyramid is a rectangle whose length and breadth are 16 cm and 12 cm, respectively. If the length of all the lateral edges passing through the vertex of the right rectangular pyramid is 26 cm, then find the volume of the pyramid in cubic centimeter.
  • a)
    1536
  • b)
    1024
  • c)
    718
  • d)
    2072
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The base of a pyramid is a rectangle whose length and breadth are 16 c...
Given Data:
Length of the rectangle base (l) = 16 cm
Breadth of the rectangle base (b) = 12 cm
Length of all lateral edges passing through the vertex (h) = 26 cm

Finding the Height of the Pyramid:
Using the Pythagorean theorem, we can find the height (h) of the pyramid.
h = √(l² + b²) = √(16² + 12²) = √(256 + 144) = √400 = 20 cm

Finding the Volume of the Pyramid:
Volume of a pyramid = (1/3) * base area * height
Base area = l * b = 16 * 12 = 192 sq. cm
Volume = (1/3) * 192 * 20 = 1280 cubic cm
Therefore, the volume of the pyramid is 1280 cubic cm, which is closest to option A (1536). The correct answer is option A.
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The base of a pyramid is a rectangle whose length and breadth are 16 cm and 12 cm, respectively. If the length of all the lateral edges passing through the vertex of the right rectangular pyramid is 26 cm, then find the volume of the pyramid in cubic centimeter.a)1536b)1024c)718d)2072Correct answer is option 'A'. Can you explain this answer?
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