Edexcel IGCSE Math B 7 mensuration

Use this Mensuration hub to move from circle sectors and arc lengths into surface area, volume, cylinders, cones and compound solids.

Covered syllabus points

7.A Length, area and volume 7.B 2D mensuration 7.C 3D mensuration 7.D Arcs and sectors

[Maximum number: 6]

Diagram NOT accurately drawn

Figure 3 shows a circle with centre O and radius 10 cm.
The points A and B lie on the circle such that $\angle A O B=100^{\circ}$ The point C is such that AC and BC are tangents to the circle.

(a)

Calculate the area, in $\mathrm{cm}^{2}$ to 3 significant figures, of OACB.

[ 3 ]

(b)

Calculate the area, in $\mathrm{cm}^{2}$ to 3 significant figures, of the region shown shaded in Figure 3.
[Area of circle $=\pi r^{2}$ ]

[ 3 ]

Sector area:
$\frac{100}{360}\times\pi\times10^{2}=87.27\ldots$
Shaded region:
$119-87.27\ldots=31.7\ldots$
Final answer:
$31.7\text{ to }31.9\text{ cm}^{2}$

[Maximum number: 2]

Figure for Question 7 Mensuration question 2 — Edexcel IGCSE Math B

Diagrams NOT accurately drawn.

Figure 3 shows a rectangle with dimensions 20 cm by 10 cm from which a square with sides of length x cm is removed from each of the corners.
The shape in Figure 3 is then folded along the dotted lines to form a box, without a lid, in the shape of a cuboid, shown in Figure 4.
The volume of the box is $V\,\mathrm{cm}^3$ .

Show that $V=4 x^{3}-60 x^{2}+200 x$

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Covered syllabus points

7 Mensuration question 1

Question (a)

Question (b)

7 Mensuration question 2