Painting surfaces

Geometry Level pending

One liter paint covers an area of 50000 square centimeters. Four spherical wooden balls (with radius 15 centimeters), six wooden cubes (with side length 30 centimeters) and six wooden cuboids (with dimensions 30 centimeters x 15 centimeters x 10 centimeters) are to be painted. How many one liter cans of paint shall be purchased if the solids are to be painted with two coatings. Use 3.14 for the approximation of π \pi .

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1 solution

The total surface area of the solids are

S = 4 ( 4 ) ( 3.14 ) ( 1 5 2 ) + 6 ( 6 ) ( 3 0 2 ) + 6 ( 2 ) [ 15 ( 30 ) + 30 ( 10 ) + 10 ( 15 ) ] = 11304 + 32400 + 10800 = 54504 S=4(4)(3.14)(15^2)+6(6)(30^2)+6(2)[15(30)+30(10)+10(15)]=11304+32400+10800=54504

n u m b e r o f c a n s = 2 ( 54504 ) 50000 ≈ number~of~cans=\dfrac{2(54504)}{50000} \approx 3 \boxed{3}

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