Solved: The volume of a hemisphere, V, is given by the formula $ V = \sqrt... [IB Mathematics Analysis and Approaches (AA)]

Question

SLPaper 1

The volume of a hemisphere, V, is given by the formula

$V = \sqrt {\frac{{4\,{T^3}}}{{243\,\pi }}}$ ,

where T is the total surface area.

The total surface area of a given hemisphere is 350 cm^2.

Calculate the volume of this hemisphere in ${\text{cm}}^3$ .

Give your answer correct to one decimal place.

[3]

Verified

Solution

474 $(\text{cm}^3)$ (A1)

Note: Follow through from part (a).

[1 mark]

Write down your answer to part (a) correct to the nearest integer.

[1]

Verified

Solution

This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$\sqrt{\frac{{4\left(350\right)^3}}{{243\pi}}}$ OR $\sqrt{\frac{{171500000}}{{763.407\ldots}}}$ (M1)

Note: Award (M1) for substitution of 350 into volume formula.

= 473.973… (A1)

= 474 (cm³) (A1)(C3)

Note: The final (A1) is awarded for rounding their answer to 1 decimal place provided the unrounded answer is seen.

[3 marks]

Write down your answer to part (b) in the form $a\times 10^k$ , where $1 \leq a \leq 10$ and $k\in\mathbb{Z}$ .

[2]

Verified

Solution

4.74 × 10²(cm³) (A1)(A1)

Note: Follow through from part (b) only. Award (A0)(A0) for answers of the type 0.474 × 10³.

[2 marks]

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