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A jumbo crayon is composed of a cylinder with a conical tip. The cylinder is 12 cm tall with a radius of 1.5 cm, and the cone has a slant height of 2 cm and a radius of 1 cm.

The lateral area of the cone is
π cm2.

To wrap paper around the entire lateral surface of the cylinder,
π cm2 of paper is needed.

The surface area, including the bottom base of the crayon, is
π cm2

User Jerson
by
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1 Answer

5 votes

Answer: 40.25π cm^2.

Explanation:

To find the lateral area of the cone, we can use the formula: Lateral Area of Cone = πrℓwhere r is the radius of the cone and ℓ is the slant height of the cone.Substituting the given values, we get:Lateral Area of Cone = π(1 cm)(2 cm) = 2π cm^2To wrap paper around the entire lateral surface of the cylinder, we need to find the lateral area of the cylinder, which can be calculated using the formula:Lateral Area of Cylinder = 2πrhwhere r is the radius of the cylinder, and h is the height of the cylinder.Substituting the given values, we get:Lateral Area of Cylinder = 2π(1.5 cm)(12 cm) = 36π cm^2To find the total surface area of the crayon, including the bottom base of the cylinder, we can use the formula:Total Surface Area = Lateral Area of Cylinder + Area of Bottom Base of Cylinder + Lateral Area of ConeThe area of the bottom base of the cylinder is simply πr^2, where r is the radius of the cylinder.Substituting the given values, we get:Area of Bottom Base of Cylinder = π(1.5 cm)^2 = 2.25π cm^2Therefore, the total surface area of the crayon is:Total Surface Area = 36π cm^2 + 2.25π cm^2 + 2π cm^2 = 40.25π cm^2So the surface area of the jumbo crayon, including the bottom base of the cylinder, is 40.25π cm^2.

User Noah Seidman
by
7.8k points