Formulas for Areas and Volumes - Mensuration Problems (Areas and Volumes Questions) - Quantitative Aptitude Questions and Quiz
Formulas for Areas and Volumes
Diameter, D = 2R
Area = πR2 sq. units
Circumference = 2πR units
Area = a2 sq. units
Perimeter = 4a units
Diagonal, d = √2 a units
Area = L*B sq. units
Perimeter = 2(L+B) units
Diagonal, d = √L2+B2 units
Right Angled Triangle:
Area = (½)bxh sq. units
Perimeter = b + h + hypotenuse
Hypotenuse = √b2+h2 units
Area = √4 a2 sq. units
Perimeter = 3a units, where a = side of the triangle
Area: √s(s-a)(s-b)(s-c) sq. units; s = (a+b+c)/2
Perimeter = (a+b+c) units
Area = b/4 √4a2-B2 sq units
Perimeter = 2a + b units, where b = base length; a = equal side length
Volume = a3 cubic units
Lateral Surface Area (LSA) = 4a2 sq. units
Total surface area (TSA) = 6a2 sq. units
Length of diagonal = a√3 units
Volume = (Cross section area * height) = L * B * H cubic units
Lateral Surface Area (LSA) = 2[(L+B)H] sq. units
Total surface area (TSA) = 2(LB+BH+HL) sq. units
Length of the diagonals = √L2+B2+H2 units
Volume = (4/3) πR3 cubic units
Surface Area = 4πR2 sq. units
If R and r are the external and internal radii of a spherical shell, then its Volume
= (4/3) [R3-r3] cubic units
Volume = (2/3) πR3 cubic units
TSA = 3πR2 sq. units
Volume = πr2h cubic units
Curved surface Area (CSA) (excludes the areas of the top and bottom circular regions) = 2πRh sq. units
TSA = Curved Surface Area + Areas of the top and bottom circular regions = 2πRh + 2πR2
= 2πR[R+h] sq. units
Volume = (1/3) πR2h cubic units
Slant Height of cone, L = √R2+H2 units
CSA = πRL sq. units
Mensuration Problems (Areas and Volumes Questions)
A right circular cone is placed over a cylinder of the same radius. Now the combined structure is painted on all sides. Then they are separated now the ratio of area painted on Cylinder to Cone is 3:1. What is the height of Cylinder if the height of Cone is 4 m and radius is 3 m?
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A smaller triangle is having three sides. Another big triangle is having sides exactly double the sides of the smaller triangle. Then what is the ratio of Area of Smaller triangle to Area of the bigger triangle?
C. 200 m² It touches on midpoints on the sides of the square ABCD
Side = √ (10² +10²) = √200
Area = 200 m²
A hemispherical bowl of diameter 16cm is full of ice cream. Each student in a class is served exactly 4 scoops of ice cream. If the hemispherical scoop is having a radius of 2cm, then ice cream is served to how many students?
A hollow cylindrical tube is made of plastic is 4 cm thick. If the external diameter is 18 cm and length of the tube is 59cm, then find the volume of the plastic?
A. 10380 cm³
B. 10384 cm³
C. 10440 cm³
D. 10444 cm³
If the ratio of radius two Cylinders A and B are in the ratio of 2:1 and their heights are in the ratio of 2:1 respectively. The ratio of their total surface areas of Cylinder A to B is?
The area of the Circular garden is 88704 m². Outside the garden a road of 7m width laid around it. What would be the cost of laying road at Rs. 2/m².
A. Rs. 7,546
B. Rs. 10,036
C. Rs. 11,092
D. Rs. 15,092