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555-605 (Medium)|   Geometry|      
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A circular microchip with a radius of 2.5 centimeters is manufactured 13 Jun 2019, 00:42
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A circular microchip with a radius of 2.5 centimeters is manufactured following a blueprint scaled such that a measurement of 1 centimeter on the blueprint corresponds to a measurement of 0.05 millimeters on the microchip. What is the area of the blueprint, in square centimeters? (1 centimeter = 10 millimeters)

(A) 25000
(B) 50000π
(C) 250,000π
(D) 100000π
(E) 625000
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C
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A circular microchip with a radius of 2.5 centimeters is manufactured 13 Jun 2019, 01:54
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Bunuel
A circular microchip with a radius of 2.5 centimeters is manufactured following a blueprint scaled such that a measurement of 1 centimeter on the blueprint corresponds to a measurement of 0.05 millimeters on the microchip. What is the area of the blueprint, in square centimeters? (1 centimeter = 10 millimeters)

(A) 25000
(B) 50000π
(C) 250,000π
(D) 100000π
(E) 625000
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1 Cm on blue print corresponds to .05 mm on chip then mm of the radius of the actual chip is 2.5cm*10=25mm, so 25mm corresponds to 25/.05 = 500 cm on blue print , SO Area = pie*250,000 IMO C
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A circular microchip with a radius of 2.5 centimeters is manufactured 13 Jun 2019, 10:38
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Bunuel
A circular microchip with a radius of 2.5 centimeters is manufactured following a blueprint scaled such that a measurement of 1 centimeter on the blueprint corresponds to a measurement of 0.05 millimeters on the microchip. What is the area of the blueprint, in square centimeters? (1 centimeter = 10 millimeters)

(A) 25000
(B) 50000π
(C) 250,000π
(D) 100000π
(E) 625000
Show more

2.5 cm = 25mm
and in blue print = 25/0.05 ; 500 mm
area - (500)^2*pi = IMO C
250,000 pi
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A circular microchip with a radius of 2.5 centimeters is manufactured 13 Jun 2019, 11:27
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10 mm = 1 cm
=> 0.05 mm = 0.005 cm
Therefore, microchip radius of 2.5 cm = blueprint radius (2.5/0.005) cm = 500 cm

So, the required area = pi*(500)^2 = 250,000 pi

IMO (C)
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A circular microchip with a radius of 2.5 centimeters is manufactured 13 Jun 2019, 12:28
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O.05mm on microchip = 1cm on blueprint or 10mm on blueprint
1mm on microchip = 10/0.05
25mm (2.5cm) on microchip = r = 10/0.05 * 25 = 5000mm = 500cm

Area on blueprint = πr*r = 250,000 cm^2

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A circular microchip with a radius of 2.5 centimeters is manufactured 28 Jun 2019, 15:17
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Chip radius is 2.5 cm
Convert to mm, Chip radius = 25 mm
Scale is .05 mm Chip = 1 cm Blueprint
Multiply by 10^2
Scale is now 5mm Chip = 100 cm Blueprint
Chip radius of 25 mm = 500 cm Blueprint radius
500^2 = 250,000
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A circular microchip with a radius of 2.5 centimeters is manufactured 15 Sep 2019, 18:26
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1cm = 0.05mm or 1cm = 0.005cm (proportions)

2.5cm/ 0.005cm = 500cm
easiest way to do this is to convert to fractions:
(5/2)/(5/1000) = 5000/10 = 500cm (this is the size of the radius on the blue print)
(500cm)^2 * pi = 250000cm^2 *pi
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A circular microchip with a radius of 2.5 centimeters is manufactured 20 Aug 2025, 02:20
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