A metal box is heated until each of its sides has expanded by 0.1%. By what percent has the volume of the box changed?

Question

BlackTom AI · Accepted Answer

We start by recognizing that the problem deals with thermal expansion in three dimensions. If each linear dimension increases by 0.1%, the fractional increase in each dimension is 0.001 (since 0.1% = 0.001 in decimal).

Option 1: '+
0.1
%' — This would imply the volume increases by 0.1%. However, the volume depends on all three dimensions, so the total fractional change in volume is approximately three times the fractional change in a single dimension for small expansions, not just the change in one dimension. Therefore, this underestimates the true volume change.

Option 2: '+
0.3
%' — This matches the first-order approximation for the volume change when each linear dimension expands by the same small fraction. Since volume scales as (1+0.001)^3 ≈ 1 + 3×0.001 = 1.003, the fractional change is about 0.3%. This option aligns with the expected three-dimensional expansion behavior.

Option 3: '−
0.3
%' — This would indicate a decrease in volume, which contradicts the fact that heating increases all linear dimensions. Therefore, a negative volume change is incorrect.

Option 4: '−
0.1
%' — This expresses a decrease of 0.1% in volume, which again contradicts the expansion of all sides. Since all sides lengthen, the volume cannot shrink in this scenario.

In sum, the physically correct interpretation for small, uniform linear expansions in three dimensions yields a positive volume change around 0.3%, while the other options either misstate the amount or imply a contraction that does not occur under heating.

SPHY001 Practice Quiz - Unit 13 | LA053

A metal box is heated until each of its sides has expanded by 0.1%. By what percent has the volume of the box changed?

查看解析

登录即可查看完整答案

类似问题

Compute 𝑌 ~ 𝑡 . Round your answer to the nearest tenth of a percent.

Given your answer to the previous question, you know that 𝑌 ~ 𝑡 = ______ percent. Round your answer to the nearest tenth of a percent.

The nominal price of a Subaru Outback changed by ______ percent between 2019 and 2024. Round your answer to the tenth of a percent.

The price of petrol was 120.8 cents per litre in January. It increased by 3.5% in February, increased by 8% in March, and decreased by 4% in April. The price of petrol per litre in May, in cents per litre, is closest to:

The monthly membership fee of the gymnasium was $95 three years ago. The fee has since had annual increases of 2.8%, 5.5% and 3.3% respectively. Total percentage increase in fees over the three years is closest to:

Compute ΔK1 K0 . Round your answer to the nearest tenth of a percent.

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单