Answer:
SA ≈ 340.26 cm²
Step-by-step 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: [tex]SA=2(lwlh+wh)[/tex]
a sphere: [tex]SA=4\pi R^2[/tex]
The formula of an area of a circle: [tex]A=\pi r^2[/tex]
The surface area of a rectangular prism:
[tex]l=6cm,\ w=10cm,\ h=6cm[/tex]
[tex]SA_1=2(6\cdot10+6\cdot6+10\cdot6)=2(60+36++60)=2(156)=312\ cm^2[/tex]
The surface area of a sphere:
[tex]R=3cm[/tex]
[tex]SA_2=4\pi(3^2)=4\pi(9)=36\pi\ cm^2[/tex]
The area of a circle:
[tex]r=3cm[/tex]
[tex]A=\pi(3^2)=9\pi\ cm^2[/tex]
The surface area of figure:
[tex]SA=SA_1-A+\dfrac{1}{2}SA_2[/tex]
Substitute:
[tex]SA=312-9\pi+\dfrac{1}{2}(36\pi)=312-9\pi+18\pi=(312+9\pi)\ cm^2[/tex]
[tex]\pi\approx3.14[/tex]
[tex]SA\approx312+9(3.14)=312+28.26=340.26\ cm^2[/tex]
