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Mary’s bedroom is an exact cube with volume measuring 1000 cubic fee

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Mary’s bedroom is an exact cube with volume measuring 1000 cubic fee  [#permalink]

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New post 22 Nov 2016, 05:49
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Mary’s bedroom is an exact cube with volume measuring 1000 cubic feet. The bedroom is furnished with a rectangular yoga mat measuring 6 feet long by 4 feet wide and a circular rug measuring 6 feet in diameter. If Mary has no other furniture in her bedroom and the yoga mat and rug do not intersect in any way, how much of her bedroom floor is NOT covered by furniture?

A. 33 square feet
B. 24+9π square feet
C. 76−9π square feet
D. 67 square feet
E. 100 square feet

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Re: Mary’s bedroom is an exact cube with volume measuring 1000 cubic fee  [#permalink]

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New post 22 Nov 2016, 06:52
Bunuel wrote:
Mary’s bedroom is an exact cube with volume measuring 1000 cubic feet. The bedroom is furnished with a rectangular yoga mat measuring 6 feet long by 4 feet wide and a circular rug measuring 6 feet in diameter. If Mary has no other furniture in her bedroom and the yoga mat and rug do not intersect in any way, how much of her bedroom floor is NOT covered by furniture?

A. 33 square feet
B. 24+9π square feet
C. 76−9π square feet
D. 67 square feet
E. 100 square feet


C

Floor area= 10*10=100 square feet
area of yoga mat= 6*4= 24 square feet
area of circular rug= π*3*3= 9π square feet
Required= 100-24-9π= 76-9π
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Re: Mary’s bedroom is an exact cube with volume measuring 1000 cubic fee  [#permalink]

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New post 22 Nov 2016, 07:52
Area of floor of room =10*10
Cube root of 1000
Area occupied by mat and rug = 6*4+pi*9
Area not occupied = 100-24-9pi hence ans c

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Re: Mary’s bedroom is an exact cube with volume measuring 1000 cubic fee  [#permalink]

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New post 22 Nov 2016, 07:54
Bunuel wrote:
Mary’s bedroom is an exact cube with volume measuring 1000 cubic feet. The bedroom is furnished with a rectangular yoga mat measuring 6 feet long by 4 feet wide and a circular rug measuring 6 feet in diameter. If Mary has no other furniture in her bedroom and the yoga mat and rug do not intersect in any way, how much of her bedroom floor is NOT covered by furniture?

A. 33 square feet
B. 24+9π square feet
C. 76−9π square feet
D. 67 square feet
E. 100 square feet


Length = Breadth = Height = 10

Floor Area = Length * Breadth

Floor Area = 10 * 10 => 100

Area of yoga mat = 6*4 = 24
Area of circular rug = π*3^2 =9π

Area of Floor not covered by yoga mat and circular rug = Total Area of Floor - ( Area of Yoga Mat + Area of circular rug )

Area of Floor not covered by yoga mat and circular rug = 100 - ( 24 + 9π ) => 76−9π

Hencem Answer will be (C) 76−9π
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Re: Mary’s bedroom is an exact cube with volume measuring 1000 cubic fee  [#permalink]

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New post 02 Aug 2017, 21:50
when the bedroom is a cube then the total surface area is 6a^2=6*(10)^2 =600
But here are we just considering the one area that is each face of the cube and so that is 10*10=100
IS my reasoning correct??
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Re: Mary’s bedroom is an exact cube with volume measuring 1000 cubic fee   [#permalink] 02 Aug 2017, 21:50
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