Question

A small lead pencil has a cylindrical base and a conical point.

Answer 1

9514 1404 393

Answer:

• slant height: 2.1 cm
• pencil area: 51.12 cm^2

Step-by-step explanation:

The slant height (s) is the hypotenuse of the right triangle with legs of 2 cm and 0.5 cm.

  s^2 = 2^2 + 0.5^2 = 4 + 0.25

  s = √4.25 ≈ 2.0616 ≈ 2.1

The slant height is about 2.1 cm.

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The surface area of the whole pencil is the sum of the areas of the circular base, the lateral area of the cylindrical part, and the lateral area of the cone.

  A = πr^2 +2πrh +πrs

  A = πr(r +2h +s) = (3.14)(0.5 cm)(0.5 cm + 2×15 cm + 2.1 cm)

  A ≈ 51.12 cm^2

The area of the whole pencil is about 51.12 cm^2.