Question
Download Solution PDFThe base of a right prism is an equilateral triangle. The lateral surface area of prism is 252 sq. cm and the volume of the prism is 147√3 cm2. Then, what is the side (in cm) of the base of the prism?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Lateral surface area of prism is 252 sq. cm
Volume of the prism is 147√3 cm2
Formula used:
Lateral surface area of prism = perimeter of base × height
Volume of the prism = Area of base × height
Calculation:
Let the side of the base of prism be a cm and height of the prism be h cm.
Lateral surface area of prism = perimeter of base × height
⇒ Lateral Surface Area of Prism = 3 × a × h = 252
⇒ ah = 252/3
⇒ ah = 84 ---- (1)
The volume of the prism = Area of base × height
⇒ 147 = 21 × a
⇒ a = 7 cm
∴, the side of the base of the prism is 7 cm.
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