h is directly proportional to r^2 Calculate a value that completes the table below. Give any decimal answers to 1 d.p mathrm(h) & mathrm(r) 56 & 4 87.5 & ?

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h is directly proportional to r^2 Calculate a value that completes the table below. Give any decimal answers to 1 d.p mathrm(h) & mathrm(r) 56 & 4 87.5 & ?

Answer 1

When \( h \) is directly proportional to \( r^{2} \), there is a constant \( k \) such that \( h=kr^{2} \). To find the constant k, we can take the value of \( h \) and \( r \) from the given information and substitute it into the formula. From the table \( k = \frac{h}{r^{2}} = \frac{56}{4^{2}} = 3.5 \). Now let's use the constant value to find the missing value of \( r \). From the formula, we know that \( r^{2} = \frac{h}{k} \). Substitute \( h = 87.5 \) and \( k = 3.5 \) into the formula, we get \( r^{2} = \frac{87.5}{3.5} = 25 \). So \( r = \sqrt{25} = 5 \) Therefore, the undetermined value of \( r \) is 5.0, which needs to be adjusted to 1 d.p., so the result becomes 5.0. ***The undetermined value of \( r \) in the given table should be 5.0 to one decimal place.***

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h is directly proportional to r^2 Calculate a value that completes the table below. Give any decimal answers to 1 d.p mathrm(h) & mathrm(r) 56 & 4 87.5 & ?

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