Question

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Question: Find the surface area of each figure. Round the answer to two decimal places. (use π = 3.14) Do not include units of measure in your answer.

Here is the picture l
l
v

Answer 1

SA ≈ 340.26 cm²

Explanation:

We have the rectangular prism 6cm × 10cm × 6cm and the semisphere with diameter D = 6cm → radius R = 3cm (6 : 2 = 3).

The surface area of given figure:

Surface area of a rectangular prism reduced by an area of a circle

+

Half of surface area of a sphere.

The formula of a surface area of

a reactangular prism:
`SA=2(lwlh+wh)`

a sphere:
`SA=4\pi R^2`

The formula of an area of a circle:
`A=\pi r^2`

The surface area of a rectangular prism:

`l=6cm,\ w=10cm,\ h=6cm`

`SA_1=2(6\cdot10+6\cdot6+10\cdot6)=2(60+36++60)=2(156)=312\ cm^2`

The surface area of a sphere:

`R=3cm`

`SA_2=4\pi(3^2)=4\pi(9)=36\pi\ cm^2`

The area of a circle:

`r=3cm`

`A=\pi(3^2)=9\pi\ cm^2`

The surface area of figure:

`SA=SA_1-A+(1)/(2)SA_2`

Substitute:

`SA=312-9\pi+(1)/(2)(36\pi)=312-9\pi+18\pi=(312+9\pi)\ cm^2`

`\pi\approx3.14`

`SA\approx312+9(3.14)=312+28.26=340.26\ cm^2`