Question
\(\begin{aligned}&\text{The diagram shows two sides, }VA\mathrm{~and~}VB,\text{ of a regular polygon.}\\&AVX\text{ is a straight line.}\\&\mathrm{Angle~}BVX=y^{\circ}\text{ and angle }AVB=11.5y^{\circ}.\\&\text{Find the number of sides of this polygon.}\end{aligned}\)
▶️Answer/Explanation
$25$
\( \angle AVB = 11.5y^\circ \)
\( \angle BVX = y^\circ \)
\( AVX \) is a straight line.
Since \( AVX \) is a straight line
$
\angle AVB + \angle BVX = 180^\circ
$
$
11.5y + y = 180
$
$
12.5y = 180
$
$
y = \frac{180}{12.5} = 14.4^\circ
$
number of sides \( n \) of the regular polygon
$
\frac{360^\circ}{y} = n
$
$
\frac{360}{14.4} = 25
$
Question
Two parcels are mathematically similar.
The larger parcel has volume 80cm$^{3}$ and height 5.2cm.
The smaller parcel has volume 33.75 cm$^{3}.$ Calculate the height of the smaller parcel.
▶️Answer/Explanation
$3.9$
For similar shapes, the ratio of volumes is the **cube** of the ratio of their corresponding lengths
$
\frac{\text{Volume of large parcel}}{\text{Volume of small parcel}} = \left( \frac{\text{Height of large parcel}}{\text{Height of small parcel}} \right)^3
$
$
\frac{80}{33.75} = \left( \frac{5.2}{h} \right)^3
$
$
\frac{80}{33.75} = 2.3704
$
$
\frac{5.2}{h} = \sqrt[3]{2.3704}
$
$
\sqrt[3]{2.3704} \approx 1.33
$
$
h = \frac{5.2}{1.33}
$
$
h \approx 3.91 \, \mathrm{cm}
$
Question
Triangle ABC is similar to triangle DEF.
Calculate the value of
(a) x,
Answer/Explanation
Ans: 7.5
(b) y,
Answer/Explanation
Ans: 12 cao
Question
Two cups are mathematically similar.
The larger cup has capacity 0.5 litres and height 8cm.
The smaller cup has capacity 0.25 litres.
Find the height of the smaller cup.
……………………………. cm
Answer/Explanation
Ans:
6.35 or 6.349 to 6.350
Question
Triangle ABC is similar to triangle PQR.
Find PQ.
PQ = …………………………………….. cm
Answer/Explanation
Ans:
9.1 oe
Question
The two barrels in the diagram are mathematically similar.
The smaller barrel has a height of hcm and a capacity of 100 litres.
The larger barrel has a height of 90cm and a capacity of 160 litres.
Work out the value of h.
h = …………………………………
Answer/Explanation
Ans:
76.9 or 76.94 to 76.95
Question
Triangle ABC is mathematically similar to triangle PQR.
Find the value of x.
x = ………………………………………….
The diagram shows two mathematically similar bowls.
The larger bowl has capacity 7.8 litres and height 11.5cm.
The smaller bowl has capacity 4 litres.
Calculate the height of the smaller bowl.
…………………………………….. cm
Answer/Explanation
(a)1.84
(b)9.20 or 9.204 or 9.205
Question
The diagram shows an open rectangular box ABCDEFGH.
AB = 18.6 cm, BC = 9cm and CG = 14.5cm.
A straight stick AGM rests against A and G and extends outside the box to M.
(a) Calculate the angle between the stick and the base of the box.
(b) AM = 30 cm.
Show that GM = 4.8cm, correct to 1 decimal place.
Answer/Explanation
35.1 or 35.05 to 35.06
\(30-\sqrt{18.6^{2}+9^{2}+14.5^{2}}
30-\frac{14.5}{sin(their(a))}\)
or
\(30-\frac{18.6^{2}+9^{2}}{cos(their(a))}\)