Mensuration is a pure formula-based topic and tricks/shortcuts are seldom applied here. So in this series I will try to solve all the mensuration problems that have appeared in CGL lately and in the process I will share the important concepts/formulas.
For Prism and Calendar (figures with uniform girth) –
Lateral Surface Area = Height * Perimeter of the Base
Volume = Height * Area of the Base
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In this question the Total surface area is being asked
Total Surface Area of a Prism = Lateral Surface Area + Area of the two bases
Height of the prism = 10 cm
Perimeter of the base = 5 + 12 + 13 (Calculate the hypotenuse with Pythagoras Theorem) = 30 cm
So Lateral Surface Area = 10 * 30 = 300 cm
Area of the base = 1/2 * base * height = 1/2 * 5 * 12 = 30 cm
So Total Surface Area = 300 + 2*30 = 360 cm
Answer : (A)
27 * (r/R)^2=H/h
Put the value of r/R from equation (1)
Put H = 30 cm
Answer : (B)
Area of triangle BDC = 84 cm (Apply Heron’s formula)
Area of base/quadrilateral = 84 + 54 = 138 cm
Volume = Height * Area of the Base
2070 = Height * 138
So, Height of the prism = 15 cm
Lateral Surface Area = Height * Perimeter of the Base
Perimeter of the base = AB + BC + CD + DA = 48 cm
Lateral Surface Area = 48 * 15 = 720 cm^2
Answer : (A)
Perimeter of the base = 3a
Volume of the prism = Area of the base * Height =√3/4 * a^2 * h … (1)
Lateral surface Area of the prism = Perimeter of the base * Height = 3a * h …(2)
Divide equation (1) by (2)
Volume/Area = (1/4√3) * a
40√3/120 = a/4√3 [Since Volume = 40√3 and Lateral surface Area = 120]
a = 160 * 3/120
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