Question
(a)
The diagram shows a quadrilateral PQRS formed from two triangles, PQS and QRS.
Calculate
(i) QR,
QR = …………………………………….. cm
(ii) PS,
PS = …………………………………….. cm
(iii) the area of quadrilateral PQRS.
…………………………………….\( cm^{2}\)
(b)
The diagram shows an open box ABCDEFGH in the shape of a cuboid.
AB = = 20 cm, BC 18 cm and AE = 16 cm.
A thin rod AGX rests partly in the box as shown.
The rod is 40cm long.
(i) Calculate GX, the length of the rod which is outside the box.
GX = …………………………………….. cm
(ii) Calculate the angle the rod makes with the base of the box.
………………………………………….
Answer/Explanation
(a)(i) 2.67 or 2.666…
(ii) 4.14 or 4.140…
(iii) 20.4 or 20.35 to 20.36…
(b)(i) 8.7[0] or 8.695…
(ii) 30.7 or 30.73 to 30.74…
Question
A solid metal cone has radius 1.65cm and slant height 4.70 cm.
(a) Calculate the total surface area of the cone.
[The curved surface area, A, of a cone with radius r and slant height l is \(A =Πrl\).]
…………………………………… \(cm^{2}\)
(b) Find the angle the slant height makes with the base of the cone.
………………………………………….
………………………………………….
(c) (i) Calculate the volume of the cone.
[The volume, V, of a cone with radius r and height h is \()V=\frac{1}{3}\pi r^{2}h\)]
…………………………………… \(cm^{3}\)
(ii) A metal sphere with radius 5cm is melted down to make cones identical to this one.
Calculate the number of complete identical cones that are made.
[The volume, V, of a sphere with radius r is \(V=\frac{4}{3}\pi r^{3}\)]
………………………………………….
Answer/Explanation
(a) 32.9 or 32.91 to 32.92…
(b) 69.4 or 69.44 to 69.45
(c)(i) 12.5 or 12.54 to 12.55
(c)(ii) 41
Question
(a) Manjeet uses 220 litres of water each day.
She reduces the amount of water she uses by 15%.
Calculate the number of litres of water she now uses each day.
………………………………….. litres
(b) Manjeet has two mathematically similar bottles in her bathroom.
The large bottle holds 1.35 litres and is 29.7cm high.
The small bottle holds 0.4 litres.
Calculate the height of the small bottle
…………………………………….. cm
(c) Water from Manjeet’s shower flows at a rate of 12 litres per minute.
The water from the shower flows into a tank that is a cuboid of length 90cm and width 75cm.
Calculate the increase in the level of water in the tank when the shower is used for 7 minutes.
…………………………………….. cm
Answer/Explanation
(a) 187
(b) 19.8
(c) 12.4 or 12.44…