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Chapter 10: Q29. (page 629)

The lateral surface area Sof a cone can be found by using the formula S=蟺rr2+h2, where r is the radius of the base and h is the height of the cone. Find the height of the cone.

Short Answer

Expert verified

The height of the given cone is12.48in.

Step by step solution

01

Step 1. Write the formula for the lateral surface area of the cone.

The lateral surface area (S) of a cone is given by:

S=蟺rr2+h2, where r is the radius of the cone and h is the height of the cone.

02

Step 2. Observe the given diagram.

The given diagram is:

From the given diagram, it can be noticed that the lateral surface area (S) of a cone is121in2 and the radius of the cone (r) is 3 in.

03

Step 3. Find the height of the cone.

Substitute 121 for S and 3 for r in the equationS=蟺rr2+h2 and solve for h.

S=蟺rr2+h2121=蟺332+h21213蟺=9+h212.84=9+h212.842=9+h22164.8656=9+h2164.8656鈭�9=h2155.8656=h2卤155.8656=h卤12.48=h

As, the height of the cone cannot be negative, thereforeh=鈭�12.48 is not possible.

The only possible value h of is 12.48.

Therefore, the height of the cone is12.48 in.

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