Question

NO LINKS!! URGENT HELP PLEASE!!

Find the surface of the figure below.​

Answer 1

324π ≈ 1017.88 square feet

Step-by-step explanation:

The given three-dimensional figure is made up of two congruent hemispheres and a cylinder.

The exposed surface area of the two congruent hemispheres is equal to the surface area of a sphere.

The surface area of the cylinder is its lateral surface area only.

The formulas for the surface area of a sphere and the lateral surface area of a cylinder are:

`\boxed{\begin{minipage}{5 cm}\underline{Surface area of a sphere}\\\\$SA=4\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius. \\ \\\end{minipage}}`
`\boxed{\begin{minipage}{5.5 cm}\underline{Lateral surface area of a cylinder}\\\\$LSA=2\pi r h$\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $h$ is the height. \\ \end{minipage}}`

Therefore, the formula for the total surface area of the given three-dimensional figure is:

`\boxed{\text{Total SA}=4\pi r^2 + 2 \pi r h}`

From observation of the given diagram, the radius is 6 ft and the height is 15 ft. Therefore, substitute r = 6 and h = 15 into the equation, and solve:

`\begin{aligned}\text{Total SA}&=4\pi (6)^2 + 2 \pi (6)(15)\\&=4\pi (36) + 2 \pi (6)(15)\\&=144\pi + 180 \pi \\&=324\pi \\&=1017.876019763...\\&=1017.88\; \sf ft^2\;(2\;d.p.)\end{aligned}`

Therefore, the total surface area of the given three-dimensional figure is 324π square feet or approximately 1017.88 square feet (rounded to the nearest hundredth).

Answer 2

• Exact surface area = 324pi square feet
• Approximate surface area = 1017.876 square feet

I used my calculator's stored version of pi.

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Step-by-step explanation:

This 3D figure is composed of...

• 2 hemispheres on either end
• 1 cylinder sandwiched in between

The surface area (SA) formula for a cylinder is

SA = 2*pi*r^2 + 2*pi*r*h

where the 2*pi*r^2 portion takes care of the circular bases, and 2*pi*r*h is the lateral surface area. We ignore the bases because they're covered up by the hemispheres.

LSA = lateral surface area of cylinder

LSA = 2*pi*r*h

LSA = 2*pi*6*15

LSA = 180pi

The exact lateral surface area of the cylinder is 180pi square feet.

Now imagine we glued the hemispheres together to form a full sphere.

SA = surface area of a sphere

SA = 4pi*r^2

SA = 4pi*6^2

SA = 144pi

Add this onto the previous result.

180pi + 144pi = 324pi represents the total exact surface area in terms of pi.

Use a calculator to find that 324pi = 1017.8760197631 approximately. I used my calculator's stored version of pi.

If you used pi = 3.14, then 324*pi = 324*3.14 = 1017.36