a pedestal is constructed in the form of the frustum of a pyramid, the sides of the square ends of the frustum being 360 cm, and 160 cm, and its slant height 260 cm. find volume, lateral surface area including the area of the top ad the cost of construction @ rs 50 per cubic metre and plastering it @rs 10 per square metre
Answers
Volume of pedestal i. e. frustum of a pyramid =h/3×(a*a+b*b+ab)
Answer:
Total Cost is Rs 1012.80
Step-by-step explanation:
Find the height:
base = (360 - 160) ÷ 2 = 100 cm
Slanted height = 260 cm
a² + b² = c²
a² + 100² = 260²
a² = 57600
a = √57600
a = 240 cm
The height is 240 cm
Convert all to m:
360 cm = 3.6 m
160 cm = 1.6 m
260 m = 2.6 m
240 m = 2.4 m
Find the volume:
Volume = h/3 ( Area1 + Area2 + √(Area1 x Area2) )
Volume = 2.4/3 ( 3.6 x 3.6 + 1.6 x 1.6 + √(3.6 x 1.6) )
Volume = 0.8(17.92) = 14.336 m³
The volume is 14.336 m³
Lateral surface area:
1 face = 1/2 (3.6 + 1.6) x 2.6 = 6.76 m²
4 faces = 6.76 x 4 = 27.04 m²
Find surface area needed to plaster:
Total surface area = 1.6 x 1.6 + 27.04
Total surface area = 29.6 m²
The total surface area is 42.56 m²
Find the cost of construction:
1 m³ = Rs 50
14.336 m³ = 50 x 14.336 = Rs 716.80
The cost of construction is Rs 716.80
Find the cost of plastering it:
1 m² = Rs 10
29.6 m² = 29.6 x 10 = Rs 296
The cost of plastering is Rs 296
Find the total cost:
Total cost = 716.80 + 296 = Rs1012.80
Answer: Total Cost is Rs 1012.80