1) Let's assume that the smaller solid has a volume of V cm^3.
Since the volume of a solid is directly proportional to the cube of its side length, we can set up a proportion using the surface areas:
(Volume of larger solid) : (Volume of smaller solid) = (Surface area of larger solid) : (Surface area of smaller solid)
162 : V = 108 : 48
Cross-multiplying and solving for V, we get:
162 * 48 = 108 * V
7776 = 108V
V = 7776 / 108
V = 72 cm^3
Therefore, the volume of the smaller solid is 72 cm^3.
2) Otiende's total pay for the month consists of his basic pay plus his commission. Let's calculate the commission first:
Commission on goods sold worth sh200,000 = 0.02 * 200,000 = sh4,000
Commission on goods sold over sh200,000 = 0.04 * (600,000 - 200,000) = sh16,000
Therefore, his total commission is sh4,000 + sh16,000 = sh20,000.
His total pay for the month is the sum of his basic pay and his commission:
Total pay = Basic pay + Commission
= 20,000 + 20,000
= sh40,000
Therefore, Otiende's total pay for that month is sh40,000.
3) The shaded region around the edges consists of three equal circular segments, each corresponding to an arc of one third of the circumference of their respective circles.
The radius of each circle can be found using the formula for the area of an equilateral triangle:
Area of equilateral triangle = (√3 / 4) * side^2
Substituting the given side length of 15 cm, we get:
Area of equilateral triangle = (√3 / 4) * 15^2 = 97.43 cm^2
Each radius will be one-third of the height of the equilateral triangle, which is also the radius of the circumcircle of the triangle. Using the formula for the radius of the circumcircle of an equilateral triangle:
Radius of circumcircle = (√3 / 3) * side
Substituting the given side length of 15 cm, we get:
Radius of circumcircle = (√3 / 3) * 15 = 8.66 cm
Since the angle of each circular segment is 120 degrees (360 degrees / 3), we can calculate the area of each segment using the formula:
Area of circular segment = (θ/360) * π * r^2
Substituting the given angle of 120 degrees and radius of 8.66 cm, we get:
Area of circular segment = (120/360) * π * (8.66)^2
= 1/3 * π * 75
= 25π
Since there are three equal circular segments, the total area of the shaded region is:
Total area of shaded region = 3 * 25π
= 75π
= 235.62 cm^2
Therefore, the area of the shaded region all around the edges is 235.62 cm^2.
1)Two similar solids have a surface area of 48cm^2 and 108cm^2 respectively. Find the volume of the smaller solid if the bigger one has a volume of 162cm^3.
2)Otiende works for a coffee processing company as a sales man.He is paid on monthly basis as per agreement below;
a)A basic pay of sh 20000 per month.
b)A commission of 2% for goods sold upto a maximum of shs 200000
c)A commission of 4% for goods sold over sh200000 in that month he sold goods worth sh600000.Calculate his total pay for that month
3)In a figure, ABC is an equilateral triangle of side 15cm.Arcs AB,BC and AC are those of circles with centres C,A and B respectively.Calculate the area of the shaded region all round the edges.
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