Calculate the cost of painting the vertical sides of a wooden pyramid 10 meters high and standing on a rhombus of diagonals 4 meters and 3 meters at the rate of Rs.3/- per square decimeter.
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Let diagonals of rhombus be: 2 a and 2 b : they are 4 m and 5 m
a = 2m and b = 2.5 m
Sides of rhombus = √(a² + b²) = 3.2 m
height h = 10m
Pyramid has 4 vertical slanting triangular faces with sides
x = √(a²+h² ) , y = √(b²+h²) and at base z = √(a²+b²)
x = 10.2 m y = 10.3 m z = 3.2 m
perimeter = 1/2 (x+y+z) = 11.85 m
area of triangular face = √s (s-x)(s-y)(s-z)
= √(11.85 * 1.65* 1.55 * 8.65)
Area of one face = 16.19 meter²
Total area of four faces = 64.76 meter²
rate = Rs 3 /decimeter² = Rs 3 * 100 / meter² as decimeter = 1/10 of meter
cost of total painting = area * rate = 64.76 * 300 = Rs 19,428.
Let diagonals of rhombus be: 2 a and 2 b : they are 4 m and 5 m
a = 2m and b = 2.5 m
Sides of rhombus = √(a² + b²) = 3.2 m
height h = 10m
Pyramid has 4 vertical slanting triangular faces with sides
x = √(a²+h² ) , y = √(b²+h²) and at base z = √(a²+b²)
x = 10.2 m y = 10.3 m z = 3.2 m
perimeter = 1/2 (x+y+z) = 11.85 m
area of triangular face = √s (s-x)(s-y)(s-z)
= √(11.85 * 1.65* 1.55 * 8.65)
Area of one face = 16.19 meter²
Total area of four faces = 64.76 meter²
rate = Rs 3 /decimeter² = Rs 3 * 100 / meter² as decimeter = 1/10 of meter
cost of total painting = area * rate = 64.76 * 300 = Rs 19,428.
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