Question
Download Solution PDFA solid cone with curved surface area twice its base area has slant height of 6√3 cm. Its height is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The curved surface area of the cone = 2 × base area of cone
Concepts used:
Formula used
Slant height (l) of cone = √r2 + h2
CSA of cone = πrl
Calculation:
Let the radius of the cone be r units.
⇒ πrl = 2πr2
⇒ l = 2r
⇒ r = 6√3/2
⇒ r = 3√3
Slant height (l) of cone = √r2 + h2
⇒ 6√32 = 3√32 + h2
⇒ h2 = 108 - 27 = 81
⇒ h = 9 cm
∴ The answer is 9 cm.
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