Mathematics: The base of a solid is the region between the curve yequals3 cosine x and the x-axis from xequals0 to x equals StartFraction pi Over 2 EndFraction . The cross sections perpendicular to the x-axis are squares with bases running from the x-axis to the curve. Find a formula for the area A(x) of the cross sections of the solid perpendicular to the x-axis.

The base of a solid is the region between the curve

shimohsen

22.01.2022

A=3(π/2)-1 au

Step-by-step explanation:

we have according to the graph that

f(x)=3

g(x)=cos(x)

Knowing A=∫|f(x)-g(x)|dx, then

$A=\int\limits^a_b (f(x)-g(x)}) \, dx\\$ ; where a=0 and b=π/2

$A=\int\limits^a_b (3-cos(x)){} \, dx$

A=(3x-sin(x)) evaluated 0 ≤ x ≤ π/2

A=(3(π/2)-sin(π/2))-(3.0-sin(0))

$A=3\frac{\pi }{2}-1$

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Alex9089435028

14.01.2021

9514 1404 393

192 cm²

Step-by-step explanation:

The total surface area is the sum of the two triangular base areas and the three rectangular lateral face areas.

SA = 2(1/2)(6 cm)(8 cm) + (6 cm +8 cm +10 cm)(6 cm) = 192 cm²

The surface area of the figure is 192 square centimeters.

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