Question

A cube is cut with 3 straight cuts . Either horizontally or vertically . What is the percent increased in the total surface area of the cube.

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Answer 1

Explanation:

Question:-

A cube is cut with 3 straight cuts . Either horizontally or vertically . What is the percent increased in the total surface area of the cube

To Find:-

Find the percent increased in the total surface area of the cube.

Solution:-

First ,

We have to find the total surface area of a cube:-

\sf\dashrightarrow \: Area = 6 \times { Edge }^{ 2 }⇢Area=6×Edge

2

\sf\dashrightarrow \: Area = 6 \times { 9a }^{ 2 }⇢Area=6×9a

2

\sf\dashrightarrow \: Area = 54 { a }^{ 2 }⇢Area=54a

2

Now ,

We have to find T.S.A of three cuboid:-

\sf\dashrightarrow \: T.S.A = 3 \times 2( 3a \times a + a \times 3a + 3a \times 3a )⇢T.S.A=3×2(3a×a+a×3a+3a×3a)

\sf\dashrightarrow \: T.S.A = 6( 15 { a }^{ 2 } )⇢T.S.A=6(15a

2

)

\sf\dashrightarrow \: T.S.A = 90 { a }^{ 2 }⇢T.S.A=90a

2

Now ,

We have to find the percent increased in the total surface area of the cube:-

\sf\dashrightarrow \: Percent = \dfrac { Increased \: in \: area \times 100 } { Initial \: percent }⇢Percent=

Initialpercent

Increasedinarea×100

\sf\dashrightarrow \: Percent = \dfrac { 3600 { a }^{ 2 } } { 54 { a }^{ 2 } }⇢Percent=

54a

2

3600a

2

\sf\dashrightarrow \: Percent = 66.6⇢Percent=66.6

Hence ,

Percentage increased is 66.6

MAY IT HELPS

Answer 2

Answer:

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