Edexcel GCSE Maths
Topic questions Ratio, proportion and rates of change Similarity, lengths, areas & volumes
30 questions · 108 marks · about 2 hours
ABC is a right-angled triangle.
AEC and ADB are straight lines. ED is parallel to CB.
Prove that triangle ABC is similar to triangle ADE.
ED = 20 cm CB = 30 cm AC = 18 cm
Work out the length of EC.
Two jars are mathematically similar.
Work out the height, hcm, of the smaller jar. Give your answer correct to 1 decimal place.
The surface area of the smaller jar is Acm2 The surface area of the larger jar is pAcm2
Find the exact value of p.
A, B and C are three solid spheres. Sphere A has a volume of 64 cm3 Sphere B has a volume of 125 cm3 The radius of sphere C is 50% of the radius of sphere B. Work out the ratio of the surface area of sphere A to the surface area of sphere C. Give your answer in the form a: b where a and b are integers.
ABC and AED are straight lines. BE and CD are parallel.
BE = 4.2 cm CD = 6.3 cm AC = 10.8 cm Work out the area of trapezium BCDE.
Also involves Ratio
ABC and DAB are similar isosceles triangles. AB = AC AD = BD BC:CD = 4: 21 Find the ratio AB:AD
ABC and DEF are two similar isosceles triangles.
DE = DF Work out the length of DE.
L, M and P are three similar solid cylinders made from the same material.
L has a mass of 64 g M has a mass of 125 g M has a total surface area of 144 cm2 P has a total surface area of 16 cm2 Work out height of cylinder L: height of cylinder M: height of cylinder P
Solid A and solid B are similar. The ratio of the height of solid A to the height of solid B is 2: 5 The volume of solid A is 12 cm3 Work out the volume of solid B.
The diagram shows triangle ABC and triangle AED.
Show that triangle ABC and triangle AED are similar.
The diagram above shows a frustum F of a cone. The frustum is made by removing a cone with height 10 cm from a solid cone with height 15 cm and base diameter 24 cm. The solid S is made by removing F from a solid hemisphere as shown in the diagram below.
The hemisphere has diameter 24 cm. Calculate the volume of solid S. Give your answer correct to 3 significant figures.
Also involves Ratio
Here are three similar triangles, ABG, ACF and ADE.
ABCD and AGFE are straight lines. AB:BC:CD = 1: 2: 3 Show that area of ABG: area of BCFG: area of CDEF = 1: 8: 27
A solid frustum is made by removing a small cone from a large cone as shown in the diagram.
The slant height of the small cone is 6 cm. The slant height of the large cone is 10 cm. The radius of the base of the large cone is 3 cm. Calculate the total surface area of the frustum. Give your answer correct to 3 significant figures.
The diagram shows two similar solid triangular prisms, A and B.
The volume of prism A is 58.806 cm3 The volume of prism B is 1587.762 cm3 The cross section of each prism is a right-angled triangle. For prism B the length of the base of the triangle is 8.1 cm the area of the triangle is 43.74 cm2 The height of the triangle for prism A is hcm. Work out the value of h.
Triangle ABC and triangle DEF are similar.
Work out the length of EF.
Work out the length of AB.
Triangle ABC and triangle DEF are similar.
Work out the length of EF.
Work out the length of AB.
A, B and C are three spheres. The volume of sphere A is 125 cm3 The volume of sphere B is 27 cm3 The ratio of the radius of sphere B to the radius of sphere C is 1: 2 Work out the ratio of the surface area of sphere A to the surface area of sphere C.
The diagram shows two right-angled triangles ACB and DEB.
AD = 9 cm DE = 2 cm DB = 6 cm Calculate the length of CB. Give your answer correct to 2 decimal places.
The diagram represents a solid cone.
The cone has a base diameter of 20 cm and a slant height of 25 cm. A circle is drawn around the surface of the cone at a slant height of 10 cm above the base. The curved surface of the cone above the circle is painted grey. Work out the area of the curved surface of the cone that is not painted grey. Give your answer as a multiple of π You must show all your working.
ABCDEF is a regular hexagon with sides of length x. This hexagon is enlarged, centre F, by scale factor p to give hexagon FGHIJK.
ABC and PQR are similar right-angled triangles.
angle ABC = angle PQR
Work out the length of PR.
Triangle EGH is congruent to triangle KGF.
HK = 10 cm. HG = 4 cm.
Work out the length of EF.
Also involves Ratio
A and B are two similar cylindrical containers.
the surface area of container A: the surface area of container B = 4: 9
Tyler fills container A with water. She then pours all the water into container B. Tyler repeats this and stops when container B is full of water.
Work out the number of times that Tyler fills container A with water. You must show all your working.
The circumference of circle B is 90% of the circumference of circle A.
Find the ratio of the area of circle A to the area of circle B.
Square E has sides of length e cm. Square F has sides of length f cm. The area of square E is 44% greater than the area of square F.
Work out the ratio e: f
Here are two rectangles.
Jim says,
“The two rectangles are similar because 8 + 4 = 12 and 6 + 4 = 10”
Is Jim correct? Explain your answer.
Three solid shapes A, B and C are similar.
The surface area of shape A is 4 cm2 The surface area of shape B is 25 cm2
The ratio of the volume of shape B to the volume of shape C is 27: 64
Work out the ratio of the height of shape A to the height of shape C. Give your answer in its simplest form.
Work out the length of DF.
Work out the length of CB.
Here are two similar solid shapes.
surface area of shape A: surface area of shape B = 3: 4
The volume of shape B is 10 cm3
Work out the volume of shape A. Give your answer correct to 3 significant figures.
The two triangles in the diagram are similar.
There are two possible values of x.
Work out each of these values. State any assumptions you make in your working.
Also involves Powers and roots
Cone A and cone B are mathematically similar. The ratio of the volume of cone A to the volume of cone B is 27: 8
The surface area of cone A is 297 cm2
Show that the surface area of cone B is 132 cm2
ABC and EDC are straight lines. EA is parallel to DB.
EC = 8.1 cm. DC = 5.4 cm. DB = 2.6 cm.
Work out the length of AE.
AC = 6.15 cm.
Work out the length of AB.
Show that these two triangles are mathematically similar.
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