which of the following 4 x4 domino covers represent two distinct hibachigrills
A. hhhhhvvh and hvvhhhhh
B. hvvhvvhhandand vvhhvvhh
C. vhvvvhvhandand hhvhvhvv
D. vvhhvvhhand hhhhvvvv
Answers
ANSWER:
i) The curved surface area of cylinderical petrol tank is 59.4 m².
ii) The steel actually used to make the tank is 95.04 m².
Step-by-step-explanation:
We have given that,
For a cylinderical petrol tank,
Diameter ( d ) = 4.2 m
∴ Radius ( r ) = d ÷ 2 = 4.2 ÷ 2 = 2.1 m
Height ( h ) = 4.5 m
We have to find,
i) Curved surface area of tank
ii) Total steel used to make tank
i)
Now, we know that,
\displaystyle{\pink{\sf\:Curved\:surface\:area\:of\:cylinder\:=\:2\:\pi\:r\:h}}Curvedsurfaceareaofcylinder=2πrh
\displaystyle{\implies\sf\:CSA_{cylinder}\:=\:2\:\times\:\dfrac{22}{\cancel{7}}\:\times\:\cancel{2.1}\:\times\:4.5}⟹CSAcylinder=2×722×2.1×4.5
\displaystyle{\implies\sf\:CSA_{cylinder}\:=\:2\:\times\:22\:\times\:0.3\:\times\:4.5}⟹CSAcylinder=2×22×0.3×4.5
\displaystyle{\implies\sf\:CSA_{cylinder}\:=\:22\:\times\:0.3\:\times\:9}⟹CSAcylinder=22×0.3×9
\displaystyle{\implies\sf\:CSA_{cylinder}\:=\:198\:\times\:0.3}⟹CSAcylinder=198×0.3
\displaystyle{\implies\sf\:CSA_{cylinder}\:=\:59.4\:m^2}⟹CSAcylinder=59.4m2
\therefore\:\underline{\boxed{\red{\sf\:Curved\:surface\:area\:of\:cylinder\:=\:59.4\:m^2\:}}}∴Curvedsurfaceareaofcylinder=59.4m2
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ii)
Now,
The tank is closed with steel.
We have to find how much steel was used to make the tank.
Now,
\displaystyle{\pink{\sf\:Total\:surface\:area\:of\:cylinder\:=\:2\:\pi\:r\:(\:r\:+\:h\:)}}Totalsurfaceareaofcylinder=2πr(r+h)
\displaystyle{\implies\sf\:TSA_{cylinder}\:=\:2\:\times\:\dfrac{22}{\cancel{7}}\:\times\:\cancel{2.1}\:(\:2.1\:+\:4.5\:)}⟹TSAcylinder=2×722×2.1(2.1+4.5)
\displaystyle{\implies\sf\:TSA_{cylinder}\:=\:2\:\times\:22\:\times\:0.3\:\times\:6.6}⟹TSAcylinder=2×22×0.3×6.6
\displaystyle{\implies\sf\:TSA_{cylinder}\:=\:22\:\times\:0.3\:\times\:13.2}⟹TSAcylinder=22×0.3×13.2
\displaystyle{\implies\sf\:TSA_{cylinder}\:=\:22\:\times\:3.96}⟹TSAcylinder=22×3.96
\displaystyle{\implies\sf\:TSA_{cylinder}\:=\:87.12\:m^2}⟹TSAcylinder=87.12m2
\therefore\:\underline{\boxed{\green{\sf\:Total\:surface\:area\:of\:cylinder\:=\:87.12\:m^2\:}}}∴Totalsurfaceareaofcylinder=87.12m2
Now, from the given condition,
\displaystyle{\pink{\sf\:Steel\:used\:to\:make\:tank\:-\:Steel\:wasted\:=\:Total\:surface\:area\:of\:cylinder}}Steelusedtomaketank−Steelwasted=Totalsurfaceareaofcylinder
\displaystyle{\implies\sf\:Steel\:used\:-\:\dfrac{1}{12}\:Steel\:used\:=\:TSA_{cylinder}}⟹Steelused−121Steelused=TSAcylinder
\displaystyle{\implies\sf\:Steel\:used\:\left(\:1\:-\:\dfrac{1}{12}\:\right)\:=\:87.12}⟹Steelused(1−121)=87.12
\displaystyle{\implies\sf\:Steel\:used\:\left(\:\dfrac{12\:-\:1}{12}\:\right)\:=\:87.12}⟹Steelused(1212−1)=87.12
\displaystyle{\implies\sf\:Steel\:used\:\times\:\dfrac{11}{12}\:=\:87.12}⟹Steelused×1211=87.12
\displaystyle{\implies\sf\:Steel\:used\:=\:\dfrac{\cancel{87.12}\:\times\:12}{\cancel{11}}}⟹Steelused=
Concept: A domino may be a tiny, black rectangular game piece with white dots. Within the game referred to as dominoes, sides of the dominoes with equal numbers square measure matched. Dominoes also are stood up to form elaborate patterns that look pretty spectacular once they’re knocked down. If you set them up right, pulling down the primary domino can knock down a bunch and even thousands of others. This use of dominoes galvanized the upshot, once one action inevitably causes others.
Find: Choose an appropriate option.
Solution: vvhhvvhh and hhhhvvvv in this hibachi grill we have four v and four h on both sides which shows 4X4 domino.
Final answer: D. vvhhvvhh and hhhhvvvv
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