Creeper asked in Science & MathematicsMathematics · 12 months ago

# Surface Area Help?

I don’t know how to solve the surface area of this.

https://imgur.com/gallery/1xntqi9

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• 12 months ago

We have one measurement in mm and one measurement in cm. We need both the same unit, so I'll convert the 45 mm measurement to 4.5 cm and solve for cm².

If you break down the shapes of each edge, you have two half-circles on the ends with diameters of 4.5 cm. Knowing that we know the radius is half of that or 2.25 cm. Two halves make a whole so we just need to find the are of one whole circle:

A = πr²

A = π(2.25)²

A = 5.0625π cm²

Then we have the rectangle on top that is 4.5 cm by 12 cm:

A = lw

A = 4.5(12)

A = 54 cm²

Then finally we have the arch on the bottom. If we can imagine pulling that off and making it flat to a single plane we have a rectangle with one side 12 cm and the other side half of the circumference of the circle. So let's start with that:

C = 2πr

We only want half of that, so:

l = 2πr / 2

l = πr

We know r:

l = π(2.25)

l = 2.25π cm

Now we have our length, multiply by width to get this area:

A = lw

A = 2.25π(12)

A = 27π cm²

5.0625π + 54 + 27π

32.0625π + 54 cm²

That's an exact value. If you want to have this as a decimal rounded to a few DP we get:

154.727 cm² (rounded to 3DP)

• 12 months ago

What you have is half of a cylinder that has been cut lengthwise. It has four surfaces:

(1) a flat rectangular surface that is 12 cm long and 45 mm (4.5 cm) wide; (2) a semicircular

flat surface at each end; their combined areas can be thought of as one circle with a

diameter of 45 mm; (3) and a curved surface whose length is 12 cm and whose width is

half the circumference of a 45 mm diameter circle.

(1) Flat Rectangular Surface

L = length = 12 cm

W = width = 45 mm = 4.5 cm

A1 = area of flat rectangular surface = to be determined

A1 = LW

A1 = 54 cm²

(2) Combined Area of Semicircular End Surfaces

D = W = diameter = 45 mm = 4.5 cm

A2 = combined area of semicircular end surfaces = to be determined

A2 = πD²/4

A2 = 15.9 cm²

(3) Area of Curved Surface

L = length = 12 cm

C = circumference of combined semicircular ends = to be determined

C = πD

C = 14.1 cm

W = C/2 = width = 7.1 cm

A3 = area of curved surface = to be determined

A3 = LW

A3 = 84.8 cm²

(4) Total Area

A4 = A1 + A2 + A3

A4 = 154.7 cm²

• 12 months ago

The surface area:

pi r h

= pi 22.5 (120) mm^2

= 8482,32 mm^2

• Lôn
Lv 7
12 months ago