The dimensions of a cuboidal room are in the ratio 4:5:6 and its total surface area is 5328m. Find the dimensions and the cost of painting it at inside at 20 per sq metre.
Answers
Answer:
The dimensions of a cuboidal room are in the ratio 4:5:6 and its total surface area is 5328m. The dimensions = 24cm, 30cm, 36cm and the cost of painting it at inside at 20 per sq metre = Rs 106560
Step-by-step explanation:
Let x be the sum of the dimensions of the cuboid.
The dimensions are in the ratio 4 : 5 : 6
The sum of the ratios is = 4 + 5 + 6 = 15
Width = 4/15x
Length = 5/15x
Height = 6/15x
Surface area of a cuboid = 2(l × w + l × h + w × h)
= 2(4/15x × 5/15x + 5/15x × 6/15x + 4/15x × 6/15x)
= 2(20/225x² + 30/225x² + 24/225x²)
= 2(20/225 + 30/225 + 24/225)x²
= 2(74/225)x²
= 148/225x²
5328 = 148/225x²
x² = 8100
x = √8100
x = 90
Width = 4/15 × 90 = 24 cm
Length = 5/15 × 90 = 30 cm
Height = 6/15 × 90 = 36 cm
The cost of painting = 20 × 5328 = Rs 106560
Answer:
The dimensions of a cuboidal room are in the ratio 4:5:6 and its total surface area is 5328m. The dimensions = 24cm, 30cm, 36cm and the cost of painting it at inside at 20 per sq metre = Rs 106560
Step-by-step explanation:
Let x be the sum of the dimensions of the cuboid.
The dimensions are in the ratio 4 : 5 : 6
The sum of the ratios is = 4 + 5 + 6 = 15
Width = 4/15x
Length = 5/15x
Height = 6/15x
Surface area of a cuboid = 2(l × w + l × h + w × h)
= 2(4/15x × 5/15x + 5/15x × 6/15x + 4/15x × 6/15x)
= 2(20/225x² + 30/225x² + 24/225x²)
= 2(20/225 + 30/225 + 24/225)x²
= 2(74/225)x²
= 148/225x²
5328 = 148/225x²
x² = 8100
x = √8100
x = 90
Width = 4/15 × 90 = 24 cm
Length = 5/15 × 90 = 30 cm
Height = 6/15 × 90 = 36 cm
The cost of painting = 20 × 5328 = Rs 106560