9514 1404 393
Answer:
24π cm²
Step-by-step explanation:
The radius and height of the cone are shown as 3 and 4, so we know the slant height is 5 (a 3-4-5 right triangle is formed by these dimensions). Then the total surface area of the cone is ...
A = πr² + πrl = πr(r +l)
A = π(3 cm)(3 cm +5 cm) = 24π cm² . . . . total area of the cone
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Additional comment
The (3, 4, 5) Pythagorean triple is one of several involving small integers that regularly appear in math problems. It is worth remembering. In case you need convincing:
3² + 4² = 5² . . . . sum of squares of sides is square of hypotenuse
9 + 16 = 25
