Give formulas for the volume and the surface area of a cone whose height h is three times its radius r.

Short Answer

Expert verified

Volume of cone isV=πr3.

Surface area of cone isS=πr210+1.

Step by step solution

01

Step 1. Standard formulas

The volume and surface area of a right circular cone of radius rand height hare

V=13πr2h

S=πrr2+h2+πr2

02

Step 2. Substitution and solution

Now given that the radius is rand the height is three times its radius means h=3rof cone

Substitute in standard formulas we get,

Volume of cone is V=13πr23r=πr3.

Surface area of cone isS=πrr2+3r2+πr2=10πr2+πr2=πr210+1.

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