Question
Download Solution PDFThe 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.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFLength of the rectangle l = 16 cm
Breadth of the rectangle b = 12 cm
Diagonal of the rectangle = √(l2 + b2) = √(122 + 162) = 20
Length of lateral edge = 26 cm
Let the height of the pyramid be H.
As we know,
(Length of lateral edge)2 = (Height of the pyramid)2 + [(Length of diagonal of the base)/2]2
262 = H2 + (20/2)2
⇒ H2 = 262 - 102
⇒ H = √576 = 24
As we know,
Volume of the pyramid = (1/3) × Area of Base × height
Volume of the pyramid = (1/3) × 16 × 12 × 24 = 1536 cm3
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