Answer:
the answer is b
Step-by-step explanation:
just took the test
Total surface area of the solid is option (B) 702 square centimeter
The surface area of a solid object is a measure of the total area that the surface of the object occupies.
Given,
The given solid consist of one cuboid and a pyramid
Surface area of the cuboid = 2(l × w + l × h + h × w)
l is the length = 10 cm
w is the width = 14 cm
h is the height = 6 cm
Surface area = 2( 10×14+10×6+6×14) =568 centimeter square
But top part is empty we have to subtract it
Area of top part = 10×14 =140 centimeter square
Subtract
568-140 =428 centimeter square
Height of the pyramid shape = [tex]\sqrt{12^{2}-7^{2} }=9.75[/tex] centimeter
Surface area of the pyramid shape [tex]=lw+l\sqrt{(\frac{w}{2} )^{2}+h^{2} }+w\sqrt{(\frac{l}{2} )^{2}+h^{2}[/tex]
l is the base length = 10 centimeter
w is the base width =14 centimeter
h is the height = 9.75 centimeter
Surface area of the pyramid shape =[tex]=10(14)+10\sqrt{(\frac{14}{2} )^{2}+9.75^{2} }+14\sqrt{(\frac{10}{2} )^{2}+9.75^{2}[/tex]
=413.43 centimeter square
Base area = 14 ×10 =140 centimeter square
Subtract it
413.43 - 140 = 273.43 centimeter square
Surface area of the solid = 428 +273.43 =701.43 ≅ 702 square centimeter
Hence, the surface area of the solid is option (B) 702 square centimeter
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