Answer:
15) 47.48 and 47.52
16) a) 27 cm²
b) 6 cm
Step-by-step explanation:
Question 15
When rounding a number, check the digit to the right of the one you're rounding to:
- If it is 0, 1, 2, 3 or 4 round down.
- If it is 5, 6, 7, 8 or 9 round up.
[tex]\begin{array}{|c|c|c|}\cline{1-3} \vphantom{\dfrac12} \sf Given & \sf 1\;decimal\;place & \sf 2\; sig\; fig \\\cline{1-3} \vphantom{\dfrac12}47.38 & 47.4 &47\\\cline{1-3} \vphantom{\dfrac12}47.42 & 47.4 &47 \\\cline{1-3} \vphantom{\dfrac12}47.48 & 47.5 & 47\\\cline{1-3} \vphantom{\dfrac12}47.52 & 47.5 & 48 \\\cline{1-3} \vphantom{\dfrac12}47.58 & 47.6 &48\\\cline{1-3} \vphantom{\dfrac12}47.62 & 47.6& 48\\\cline{1-3} \end{array}[/tex]
Therefore, the two numbers that are equal when they are rounded to one decimal place, and are not equal when rounded to two significant figures are:
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Question 16
Part (a)
[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a triangle}\\\\$A=\dfrac{1}{2}bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base \\ \phantom{ww}$\bullet$ $h$ is the height\\\end{minipage}}[/tex]
From inspection of the given diagram:
Substitute the found values of b and h into the formula for area of a triangle:
[tex]\begin{aligned}\implies \sf Area & = \frac{1}{2} \cdot 9 \cdot 6\\\\&=\frac{9}{2} \cdot 6\\\\&=27\;\; \sf cm^2\end{aligned}[/tex]
Therefore, the area of the triangular cross-section of the prism is:
Part (b)
[tex]\boxed{\text{$\vphantom{\dfrac12}$Volume of a prism = base area $\times$ height}}[/tex]
The bases of a prism are the two congruent polygons.
Therefore, the bases of a triangular prism are the triangles.
Given:
- Base area = 27 cm² (from part a)
- Height = 8 cm
Substitute the found base area and height into the formula for volume:
[tex]\begin{aligned}\implies \textsf{Volume of the triangular prism}& = 27 \times 8\\& = 216\;\; \sf cm^3\end{aligned}[/tex]
Therefore, the volume of the triangular prism is:
[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Volume of a cube}\\\\$V=s^3$\\\\where:\\ \phantom{ww}$\bullet$ $s$ is the side length \\\end{minipage}}[/tex]
If the volume of the rectangular prism is the same as the volume of the cube:
[tex]\implies s^3=216[/tex]
[tex]\implies \sqrt[3]{s^3}=\sqrt[3]{216}[/tex]
[tex]\implies s=6\;\; \sf cm[/tex]
Therefore, the length of one side of the cube is:
