Question
Download Solution PDFThe base of a right pyramid is an equilateral triangle whose side is 8 cm. If the volume of the pyramid is 96 cm3, find the height of the pyramid?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Side of Base triangle = 8 cm
Volume of pyramid = 96 cm3
Concept:
Using the formula of volume of the pyramid, calculate the height.
Formula used:
The volume of the pyramid = (1/3) × (Area of base) × height
Area of equilateral triangle = (√3/4) × (side)2
Calculation:
Let, the Height of the pyramid (OD) = ‘h’
Area of equilateral triangular base = (√3/4) × 8 × 8
⇒ 16√3 cm2
Now, Volume of pyramid = (1/3) × (Area of base) × height
⇒ 96 = (1/3) × 16√3 × h
⇒ h = (96 × 3)/16√3
⇒ h = 18/√3 cm
⇒ h = 6√3 cm
∴ The required height is 6√3 cm.
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