Question

একটি ঘনকের প্রত্যেকটি ধারের দৈর্ঘ্য 50% বৃদ্ধি পেলে, ঘনকটির সমগ্রতলের ক্ষেত্রফল শতকরা কত বৃদ্ধি পাবে।​

Answer 1

125%

• A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The word "percent" is used to symbolise it.
• There is no dimension to percentages. As a result, it is known as a dimensionless number. We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100. The original number is subtracted from the new number, divided by the original number, then multiplied by 100 to get the % increase.

Here, according to the given information,

Let x be a side of the cube.

Then, the total surface area is $6x^{2}$.

Now, when the edge is 100, the edge becomes 150.

When the edge is 1, it becomes $\frac{150}{100}$.

When the edge is x, it becomes $\frac{15x}{10}$.

Now, total surface area becomes $6.\frac{225x^{2} }{100}$.

Then, increase in total surface area = $6.\frac{225x^{2} }{100}- 6x^{2}=6(\frac{125x^{2} }{100} )$

Then, percentage increase in total surface area = 125%

Hence, the percentage increase is 125%

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