CAIE IGCSE Mathematics Extended 5 Mensuration Topic Practice

Calculate the area of the trapezium.

NOT TO SCALE

The diagram shows a sector of a circle with radius 8 cm and angle $75^{\circ}$.
Find the perimeter of the sector.
cm

NOT TO SCALE

The diagram shows a shape ABQP made from three straight lines and an arc of a sector of a circle. The sector has centre O and angle $90^{\circ}$.
POQ is a straight line and $A P=P O=O Q=Q B=5 \mathrm{~cm}$.
Find the area of ABQP.
Give your answer in the form $a+k \pi$.
$\mathrm{cm}^{2}$

NOT TO SCALE

Triangle ABC is mathematically similar to triangle PQR.
The area of triangle ABC is $16 \mathrm{~cm}^{2}$.

A cylinder with radius 6 cm and height $h \mathrm{~cm}$ has the same volume as a sphere with radius 4.5 cm. Find the value of h.
[The volume, V, of a sphere with radius r is $V=\frac{4}{3} \pi r^{3}$.]

A solid metal cube of side 20 cm is melted down and made into 40 solid spheres, each of radius $r \mathrm{~cm}$.

Find the value of r.
[The volume, V, of a sphere with radius r is $V=\frac{4}{3} \pi r^{3}$.]

A solid cylinder has radius $x \mathrm{~cm}$ and height $\frac{7 x}{2} \mathrm{~cm}$.

The surface area of a sphere with radius $R \mathrm{~cm}$ is equal to the total surface area of the cylinder.
Find an expression for R in terms of x.
[The surface area, A, of a sphere with radius r is $A=4 \pi r^{2}$.]