5.2 Two concentric circles have radii 7cm and 4cm respectively. PQ, a chord to the larger circle, is 13cm.
1 answer:
Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. The length of the smaller chord AB is 4 cm.
<h3>What are Similar Figures?</h3>Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".
The diagram for the given condition can be drawn as shown below. Therefore, the measure of the smaller chord AB can be found as shown below.
The two triangles, ΔOPQ and ΔOAB are similar. Therefore, for similar triangles, we can write,
Now, we can write further,
AB = 7.43 cm
Hence, the length of the smaller chord AB is 4 cm.
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Answer:
890 beads can be fitted in the triangular prism.
Step-by-step explanation:
If we can fill the spherical beads completely in the triangular prism,
Volume of the triangular prism = Volume of the spherical beads
Volume of triangular prism = Area of the triangular base × Height
From the picture attached,
Area of the triangular base =
=
By applying Pythagoras theorem in the given triangle,
AC² = AB² + BC²
(13)² = 5² + BC²
169 = 25 + BC²
BC² = 144
BC = 12
Area of the triangular base =
= 30 cm²
Height of the triangular prism = 18 cm
Volume of the triangular prism = 30 × 18
= 540 cm³
Volume of one spherical bead =
=
= 0.606 cm³
Let there are 'n' beads in the triangular prism,
Volume of 'n' beads = Volume of the prism
540 = 0.606n
n = 890.90
n ≈ 890
Therefore, 890 beads can be fitted in the triangular prism.
