The diameter of the base of a cone is 12 meters, and its height is 15 meters. Find the surface area of the cone.

The given value are

d = 12 m and h = 15 m

radius \$r = d/2\$

⇒ \$r = 12/2\$
⇒ r = 6 m

First, find the base area

\$Area of base = πr^2\$

Now the plug the values in the formula

⇒ \$"Area" "of" "base" = π(6)^2\$
⇒ Area of base = 36π

The lateral surface area is

\$"Lateral surface area" = πrl\$

To find l, by using Pythagorean theorem

⇒ \$"l" = \sqrt((r)^2 + (h)^2)\$
⇒ \$"l" = \sqrt((6)^2 + (15)^2)\$
⇒ \$"l" = \sqrt(36 + 225)\$
⇒ \$"l" = \sqrt(261)\$
⇒ l = 16.15 m

Now plug the values in the formula

⇒ \$"Lateral surface area" = π times 6 times 16.15\$
⇒ Lateral surface area = 304.266 sq.ft

Surface area of cone is

\$"Surface Area of Cone" = "Area of Base" + "Lateral Surface Area"\$

Now plug the values in the formula

⇒ Surface Area of Cone = 36π + 304.266
⇒ Surface Area of Cone = 417.306 sq.m

So, the surface area of the cone is approximately 417.306 square meters.

Can you summarize what you’ve understood in the above steps?

This is wrong calculation using the formula

417.036 sq.m

This is correct. It is accurately done the calculation by using the formula

417.306 sq.m

This is wrong calculation using the formula

417.063 sq.m

This is wrong calculation using the formula

417.360 sq.m

Option

B

Can you summarize what you’ve understood in the above steps?