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A suitcase with measures 80cm X 48cm X 24cm is to be covered with a tarpaulin cloth.How many metres of tarpaulin of width 96cm is required to cover 100 such suitcases?
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A suitcase with measures 80cm X 48cm X 24cm is to be covered with a ta...
Dimensions of a Suitcase
To determine how much tarpaulin is needed to cover one suitcase, we first calculate the surface area of a single suitcase with dimensions 80cm x 48cm x 24cm.
Surface Area Calculation
The formula for the surface area (SA) of a rectangular box is:
\[ SA = 2(lb + bh + hl) \]
Where:
- \( l \) = length = 80 cm
- \( b \) = breadth = 48 cm
- \( h \) = height = 24 cm
Calculating each component:
- \( lb = 80 \times 48 = 3840 \, \text{cm}^2 \)
- \( bh = 48 \times 24 = 1152 \, \text{cm}^2 \)
- \( hl = 24 \times 80 = 1920 \, \text{cm}^2 \)
Now, substituting into the surface area formula:
\[ SA = 2(3840 + 1152 + 1920) = 2(6912) = 13824 \, \text{cm}^2 \]
Total Surface Area for 100 Suitcases
To find the total surface area for 100 suitcases:
\[ Total \, SA = 100 \times 13824 \, \text{cm}^2 = 1382400 \, \text{cm}^2 \]
Conversion to Square Metres
Now, convert the total surface area from cm² to m² (1 m² = 10,000 cm²):
\[ Total \, SA \, in \, m² = \frac{1382400}{10000} = 138.24 \, m² \]
Calculating the Length of Tarpaulin Required
Given the width of the tarpaulin is 96 cm (0.96 m), we can find the length required using the formula:
\[ Length = \frac{Total \, SA}{Width} \]
Calculating the length:
\[ Length = \frac{138.24 \, m²}{0.96 \, m} \approx 144 \, m \]
Conclusion
To cover 100 suitcases, approximately 144 metres of tarpaulin cloth is required.
To determine how much tarpaulin is needed to cover one suitcase, we first calculate the surface area of a single suitcase with dimensions 80cm x 48cm x 24cm.
Surface Area Calculation
The formula for the surface area (SA) of a rectangular box is:
\[ SA = 2(lb + bh + hl) \]
Where:
- \( l \) = length = 80 cm
- \( b \) = breadth = 48 cm
- \( h \) = height = 24 cm
Calculating each component:
- \( lb = 80 \times 48 = 3840 \, \text{cm}^2 \)
- \( bh = 48 \times 24 = 1152 \, \text{cm}^2 \)
- \( hl = 24 \times 80 = 1920 \, \text{cm}^2 \)
Now, substituting into the surface area formula:
\[ SA = 2(3840 + 1152 + 1920) = 2(6912) = 13824 \, \text{cm}^2 \]
Total Surface Area for 100 Suitcases
To find the total surface area for 100 suitcases:
\[ Total \, SA = 100 \times 13824 \, \text{cm}^2 = 1382400 \, \text{cm}^2 \]
Conversion to Square Metres
Now, convert the total surface area from cm² to m² (1 m² = 10,000 cm²):
\[ Total \, SA \, in \, m² = \frac{1382400}{10000} = 138.24 \, m² \]
Calculating the Length of Tarpaulin Required
Given the width of the tarpaulin is 96 cm (0.96 m), we can find the length required using the formula:
\[ Length = \frac{Total \, SA}{Width} \]
Calculating the length:
\[ Length = \frac{138.24 \, m²}{0.96 \, m} \approx 144 \, m \]
Conclusion
To cover 100 suitcases, approximately 144 metres of tarpaulin cloth is required.
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A suitcase with measures 80cm X 48cm X 24cm is to be covered with a tarpaulin cloth.How many metres of tarpaulin of width 96cm is required to cover 100 such suitcases?
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A suitcase with measures 80cm X 48cm X 24cm is to be covered with a tarpaulin cloth.How many metres of tarpaulin of width 96cm is required to cover 100 such suitcases? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A suitcase with measures 80cm X 48cm X 24cm is to be covered with a tarpaulin cloth.How many metres of tarpaulin of width 96cm is required to cover 100 such suitcases? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A suitcase with measures 80cm X 48cm X 24cm is to be covered with a tarpaulin cloth.How many metres of tarpaulin of width 96cm is required to cover 100 such suitcases?.
A suitcase with measures 80cm X 48cm X 24cm is to be covered with a tarpaulin cloth.How many metres of tarpaulin of width 96cm is required to cover 100 such suitcases? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A suitcase with measures 80cm X 48cm X 24cm is to be covered with a tarpaulin cloth.How many metres of tarpaulin of width 96cm is required to cover 100 such suitcases? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A suitcase with measures 80cm X 48cm X 24cm is to be covered with a tarpaulin cloth.How many metres of tarpaulin of width 96cm is required to cover 100 such suitcases?.
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