Question

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
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leaving brainly take points ​

Answer 1

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 2

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The cost of construction is Rs 1012.80.

Slant height = 260 cm (Given)

Square ends of frustum = 360 cm and 160 cm {Given}

Base = (360 - 160)/2 => 100 cm

Slant height = a² + b² = c²

a² + 100² = 260²

a² = 57600

a = √57600

a = 240 cm

Therefore, height is 240 cm

Volume = h/3 ( Area 1 + Area 2 + √ Area 1 x Area 2

= 2.4/3 ( 3.6 x 3.6 + 1.6 x 1.6 + √(3.6 x 1.6) )

= 0.8 ( 17.92) = 14.336 m³

Therefore, the volume is 14.336 m³

Lateral surface area -

For one face = 1/2 × (3.6 + 1.6) x 2.6 = 6.76 m²

For four faces = 6.76 x 4 = 27.04 m²

Surface area needed to plaster:

= 1.6 x 1.6 + 27.04

= 29.6 m²

The total surface area is 42.56 m²

Cost of construction - 1 m³ = Rs 50

14.336 m³ = 50 x 14.33

= Rs 716.80

The cost of construction is Rs 716.80

Cost of plastering - 1 m² = Rs 10

Thus, for 29.6 = 29.6 x 10 = Rs 296

The cost of plastering is Rs 296

Total cost: = 716.80 + 296

= Rs 1012.80

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