1 Answer

Redconservatory · Answer 1 · 2021-11-15T18:41:36+0000

Answer: A=276.52 cm²

Explanation:

To find the surface area of the figure, we can find the surface area of the rectangular prism and hemisphere. Then we would add them together.

Rectangular Prism

A=2(lw+hl+hw)

Since we are given the length, width, and height, we can directly plug them into the equation and solve.

A=2((10*5)+(4*10)+(4*5))

A=2(50+40+20)

A=2(110)

A=220 cm^2

The surface area for the rectangular prism is 220 cm².

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Hemisphere

A=2πr²

This formula above is derived from the formula for surface area of a sphere.

The surface area of a sphere is A=4πr². Since the picture displays half of a sphere, we divide that by 2. This gives us A=2πr².

Since we have the radius, all we have to do is plug it in.

$A=2\pi (3)^2$

$A=2\pi (9)$

$A=18\pi$

A=56.52 cm^2 *Note I used 3.14 instead of π.

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Now that we have the surface area of the hemisphere and rectangular prism, we add them together to find the surface area of the entire prism.

A=220+56.52=276.52 cm²

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