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Tresset [83]
2 years ago
13

I need help with this work

Mathematics
1 answer:
STatiana [176]2 years ago
7 0

Answer:

G. 245.04cm²

Step-by-step explanation:

The shortest way to solve this problem would be:

total surface area = 2 * π * r² + (2 * π * r) * h

or

total surface area = 2 * π * r * (r + h).

Diameter = 6

Radius = 3

Height = 10

The radius is half the diameter

TSA = Total surface area

TSA = 2 π 3(3+10)

TSA = (2)(3.141593)(3)(3+10)

TSA = (6.283185)(3)(3+10)

TSA = 18.849556(3+10)

TSA = (18.849556)(13)

TSA = 245.044227

TSA = 245.04

Or you could do the longer way, which would be:

Step 1: Find the surface area of the curved part of the cylinder

Surface Area (Curved) = 2 x π x Radius x Height

Step 2: Find the surface area of the two ends of the cylinder

Surface Area (Ends) = 2 x π x Radius²

Step 3: Add the surface are of the curved part to the surface area of the ends

Surface Area (Total) = Surface Area (Curved) + Surface Area (Ends)

For the cylinder in the picture:

A cylinder has a height of 10 and a diameter of 6

Hence, Radius = d/2 = 6/2 = 3 cm

Surface Area (Curved) = 2 x pi x 3 x 10

Surface Area (Curved) = 188.495559

Surface Area (Ends) = 2 x pi x 3²

Surface Area (Ends) = 2 x pi x 25

Surface Area (Ends) = 56.548668

Surface Area (Total) = 245.044227

245.04 is the result of rounding 245.044227 to the nearest hundredth

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Answer:

<u><em>The area increase by 225%</em></u>

<em><u>Step-by-step explanation: </u></em>

<em><u>attachment of a triangle</u></em>

<em><u>The area of a triangle equilateral is calculated with the next formula:</u></em>

<em><u>A=\frac{a*h}{2}</u></em>

<em><u>h^{2} +(\frac{a}{2})^{2}=a^{2}</u></em>

<em><u>h^{2} = a^{2} - \frac{a^{2} }{4}= \frac{a^{2} }{4}*3</u></em>

<em><u>h=\sqrt{\frac{a^{2}*3 }{4} }</u></em>

<em><u>h=\frac{\sqrt{3}*a }{2}</u></em>

<em><u>replacing in the A equation:</u></em>

<em><u>A=\frac{a*\sqrt{3}*a }{2*2}</u></em>

<em><u>A=\frac{\sqrt{3}*a^{2} }{4}</u></em>

<em><u>Now each side increse by 50% ⇒ a=1.5a</u></em>

<em><u>A= \frac{\sqrt{3}*(1.5a)^{2} }{4}</u></em>

<em><u>A=\frac{\sqrt{3}*a^{2}* 2.25 }{4}</u></em>

<em><u>A=2.25 * \frac{\sqrt{3}*a^{2} }{4}</u></em>

<em><u>It means that the area incrase by 225%</u></em>

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