Collin's Cambridge IGCSE Maths
Student's book by Chris Pearce

Maths Question:
page 517
Exercise 27M, Question 5

Lead has a density of 11.35 g/cm3. Calculate the maximum number of lead spheres of radius 1.5 mm that can be made from 1 kg of lead.

Volume of Sphere

6231 spheres can be made from 1 kg of lead

Step-by-step explanation:

Given Density of lead d = 11.35 gm/cm³

Let the maximum number of spheres that can be made with 1 kg of lead = n

Radius of sphere r = 1.5 mm = 0.15 cm

Volume of Sphere =

Volume of one sphere V = (4/3) * 22.7 * r³

Volume of n spheres = n * (4/3) * 22.7 *r³    ….. Eq (1)

Total mass of lead m = 1kg = 1000gm ...Eq (2)

Equating the above two equations

n × V × d = m

n × (4/3) × 22.7 × ( 0.15 )³ = 1000

Therefore calculating n= 6231.45

But considering the whole number, 6231 spheres can be made from 1 kg of lead.

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c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.