Respuesta :
Answer:
So tripling the radius triples the lateral surface area involves the square of the radius. (b) tripling the radius multiplies the lateral surface area by 3, because the formula for the lateral surface area, , only involves the radius to the first power.
Step-by-step explanation:
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We have that the tripled the radius will affects the surface area of the right cylinder by giving a new equation as follows
[tex]A=2(A_1)+9 \pi r^2[/tex]
From the question we are told that:
Effect of tripled radius on right cylinder
Generally, the equation for Area of a right cylinder is mathematically given by
[tex]A=A_l+2A_b[/tex]
Where
[tex]A_l=Lateral\ Area\\\\A_b= Area\ of\ bases[/tex]
Therefore
[tex]A=2 \pi rh+2\pi r^2[/tex]
Now with radius tripled
[tex]A=2 \pi (3r)h+2\pi (3r)^2[/tex]
[tex]A=2 \pi (3r)h+2(3\pi (r)^2)+2(3\pi (r)^2)[/tex]
[tex]A=2(A_1)+9 \pi r^2[/tex]
In conclusion
The tripled the radius will affects the surface area of the right cylinder by giving a new equation as follows
[tex]A=2(A_1)+9 \pi r^2[/tex]
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