MATH SOLVE

3 months ago

Q:
# 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.

Accepted Solution

A:

Answer:Part 1) The lateral area of the cone is [tex]LA=2\pi\ cm^{2}[/tex]Part 2) The lateral surface area of the cylinder is [tex]LA=36\pi\ cm^{2}[/tex]Part 3) The surface area of the crayon is [tex]SA=41.50\pi\ cm^{2}[/tex]Step-by-step explanation:Part 1) Find the lateral area of the cone The lateral area of the cone is equal to[tex]LA=\pi rl[/tex]we have[tex]r=1\ cm[/tex][tex]l=2\ cm[/tex]substitute[tex]LA=\pi (1)(2)[/tex][tex]LA=2\pi\ cm^{2}[/tex]Part 2) Find the lateral surface area of the cylinderThe lateral area of the cylinder is equal to[tex]LA=2\pi rh[/tex]we have[tex]r=1.5\ cm[/tex][tex]h=12\ cm[/tex]substitute[tex]LA=2\pi (1.5)(12)[/tex][tex]LA=36\pi\ cm^{2}[/tex]Part 3) Find the surface area of the crayonThe surface area of the crayon is equal to the lateral area of the cone, plus the lateral area of the cylinder, plus the top area of the cylinder plus the bottom base of the crayonFind the area of the bottom base of the crayon[tex]A=\pi[r2^{2}-r1^{2}][/tex]wherer2 is the radius of the cylinderr1 is the radius of the conesubstitute[tex]A=\pi[1.5^{2}-1^{2}][/tex][tex]A=1.25\pi\ cm^{2}[/tex]Find the area of the top base of the cylinder[tex]A=\pi(1.5)^{2}=2.25\pi\ cm^{2}[/tex]Find the surface area[tex]SA=2\pi+36\pi+2.25\pi+1.25\pi=41.50\pi\ cm^{2}[/tex]