CIE Extended Mathematics (2017-18) Mensuration

Mensuration

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11	$( 2018/$m/42/img/q2$) $ The vertices of a square $ABCD$ lie on the circumference of a circle, radius 8 cm. (a) Calculate the area of the square.cm$^2[2]$ (b) (i) Calculate the area of the shaded segment cm$^2[3]$ (ii) Calculate the perimeter of the shaded segment cm [4]
12	$( 2017/$w/21/img/q20$) $ $(\mathbf{a})$ A cylinder has height 20 cm. The area of the circular cross section is 74 cm$^{2}$ Work out the volume of this cylinder. $\mathrm{cm}^{3}\left[1\right]$ (b) Cylinder $A$ is mathematically similar to cylinder $B$ The height of cylinder $A$ is 10 cm and its surface area is 440 cm$^{2}$ The surface area of cylinder $B$ is 3960cm$^{2}$ Calculate the height of cylinder $B.$ cm [3]
13	$( 2018/$w/21/img/q10$) $ A water tank in the shape of a cuboid has length 1.5 metres and width l metre. The water in the tank is 60 centimetres deep. Calculate the number of litres of water in the tank. litres[3]
14	$( 2017/$m/22/img/q9$) $ The diagram shows a pyramid with a square base $ABCD.$ All the sloping edges of the pyramid are 20cm long and $AC=17$ cm. Calculate the height of the pyramid. cm [3]
15	$( 2018/$s/22/img/q14$) $ The diagram shows a solid cuboid with base area 7 cm$^{2}$ The volume of this cuboid is 21 cm$^{3}$. Work out the total surface area. cm$^2[3]$
16	$( 2018/$s/22/img/q15$) $ Find the volume of a cylinder of radius 5 cm and height 8 cm. Give the units of your answer.[3]
17	$( 2018/$w/22/img/q22$) $ The diagram shows a cuboid with dimensions 5.5 cm, 8cm and 16.2 cm. Calculate the angle between the line $AB$ and the horizontal base of the cuboid. [4]
18	$( 2017/$s$/23/$img$/$q$5) $ Calculate the volume of a hemisphere with radius 3.2 cm. [The volume, $V$, of a sphere with radius $r$ is $V=\frac{4}{3}\pi r^{3}.]$ [2]
19	$( 2017/\mathrm{s/41/img/q5a) }$ (a) The diagram shows a cylindrical container used to serve coffee in a hotel. The container has a height of 50cm and a radius of 18 ctm. (i) Calculate the volume of the cylinder and show that it rounds to 50 900 cm$^{3}$, correct to 3 significant [2] (ii) 30 litres of coffee are poured into the container. Work out the height, $h$, of the empty space in the container $h=\ldots.........$cm[3] (iii) Cups in the shape of a hemisphere are filled with coffee from the container. The radius of a cup is 3.5 cm. Work out the maximum number of these cups that can be completely filled from the 30 litres of coffee in the container. [The volume, $V$, of a sphere with radius $r$ is $V=\frac{4}{3}\pi r^{3}.]$ [4] (b) The hotel also uses glasses in the shape of a cone. The capacity of each glass is 95 cm$^{3}.$ (i) Calculate the radius, $r$ and show that it rounds to 3.3 cm, correct to l decimal place, [The volume, $V$, of a cone with radius $r$ and height $h$ is $V=\frac{1}{3}\pi r^{2}h.]$ [3] (ii) Calculate the curved surface area of the cone. [The curved surface area, $A$ of a cone with radius $r$ and slant height $l$ is $A=\pi rl$ . cm$^2\left[4\right]$
20	$( 2017/\mathrm{w/41/img/q8a) }$ The diagram shows a solid made from a hemisphere and a cone. The base diameter of the cone and the diameter of the hemisphere are each 5 mm. (a) The total surface area of the solid is $\frac {115\pi}4\mathrm{mm^{2}.}$ Show that the slant height, $l$ is 6.5 mm. t height $l$ is $A=\pi rl.]$ [The curved surface area, $A$ of a cone with radius $r$ and slant height $l$ is $A=\pi rl.]$ [The surface area, $A$, of a sphere with radius $r$ is $A=4\pi r^2.]$ [4] (b) Calculate the height, $h$, of the cone. $h=...................mm~[3]$ (c) Calculate the volume of the solid. [The volume, $V$ of a cone with radius $r$ and height $h$ is $V=\frac{1}{3}\pi r^{2}h.]$ [The volume, $V$ of a sphere with radius $r$ is $V=\frac{4}{3}\pi r^{3}.]$ [4] (d) The solid is made from gold 1 cubic centimetre of gold has a mass of 19.3 grams. The value of 1 gram of gold is $38.62 . Calculate the value of the gold used to make the solid [3]