Mathematics: Asap you 1. find the area of the composite figure. 40 units2 38.5 units2 39.75 units2 44 units2 #2: the cylinder below needs to be spray-painted. find the surface area and use π = 3.14. round to nearest hundredth. 282.62 cm2 207.24 cm2 226.08 cm2 304.25 cm2 #3: what is the volume of a sphere with a surface area of 196 π ft2 ? 1372/ 3 π ft3 457/ 3 π ft3 226/ 3 π ft3 420 π ft3

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Asap you 1. find the area of the composite figure.

Ответ:

carterh166

09.01.2022

1: Refer to the attached image. We can split the composite figure in easy figures: triangles ABC and CDE have a base AC=4 and height of 3. Their area is thus

$A_{ABC}=A_{CDE}=\dfrac{4\cdot 3}{2}=6$

Rectangle AEFH has sides AE=8 and AH=3. So, it has area

$A_{AEFH}=8\cdot 3=24$

Finally, triangle FGH has a base HG=2 and height HF=8. So, its area is

$A_{FGH}=\dfrac{2\cdot 8}{2}=8$

So, the total area is

$A_{ABC}+A_{CDE}+A_{AEFH}+A_{FGH}=6+6+24+8=44$

The base radius is 3, so the base area is

$\pi 3^2 = 9\pi$

The lateral area is the product between the height and the base circumference:

$9\cdot 6\pi=54\pi$

So, the total area is twice the base area plus the lateral area:

$54\pi+18\pi=62\pi\approx 72\cdot 3.14=226.08$

The surface area of a sphere is

$S=4\pir^2$

Solving for r, we have

$r=\sqrt{\dfrac{S}{4\pi}}=\sqrt{\dfrac{196\pi}{4\pi}}=\sqrt{49}=7$

The volume of a sphere is

$\dfrac{4}{3}\pi r^3 = \dfrac{4}{3}\pi 7^3=\dfrac{1372}{3}\pi$

Asap you 1. find the area of the composite figure. 40 units2 38.5 units2 39.75 units2 44 units2 #2:

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