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Practice Mensuration Questions and Answers

A circular clock has the hour hand of length 6 inch. Find the length of the distance it covers by it's tip from 9 p.m. to 3 a.m.
If sin (A + B) = cos (A + B), what is the value of tan A?
If the 4-digit number x67y is exactly divisible by 9, then the least value of (x + y) is _____.
Ratio of length to width of a rectangular field is 4:3. If the perimeter of the field is 140 metres, then find the area (in m2) of the field.
Ratio of length to width of a rectangular field is 7:4. If the perimeter of the field is 220 metres, then find the area (in m2) of the field.
Ratio of length to width of a rectangular field is 2:3. If the perimeter of the field is 380 metres, then find the area (in m2) of the field.
Ratio of length to width of a rectangular field is 5:4. If the perimeter of the field is 360 metres, then find the area (in m2) of the field.
Ratio of length to width of a rectangular field is 4:7. If the perimeter of the field is 440 metres, then find the area (in m2) of the field.
If x – y = 1 and x2 + y2 = 41 where x, y ≥ 0, then the value of x + y will be:
Three circles of radius 6 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?
Number p is 15% more than 150. If k is 15% less than p, then k is equal to:
If ∆ ABC~∆ FDE such that AB = 9 cm, AC = 11 cm, DF = 16 cm and DE = 12 cm, then the length of BC is:
tan(θ -14π) is equal to:
In an equilateral triangle ABC, D is the midpoint of side BC. If the length of BC is 8 cm, then the height of the triangle is:
Find the mean proportion between (6 + √8) and (3 – √2).
The curved surface area of the sphere is 154 cm2 . Find the volume of the sphere (rounded off to one digit after decimal).
In triangle ABC, the bisector of angle BAC cuts the side BC at D. If AB = 10 cm, and AC = 14 cm then what is BD : BC ?
In triangle ABC, AD is the angle bisector of angle A. If AB = 8.4 cm and AC = 5.6 cm and DC = 2.8 cm, then the length of side BC will be:
Find the number of common tangents, if r1 + r2 = C1C2 .(With usual notations, r1 & r2 and C1 & C2 are the radii and centres of the two circles.)
The length of the side of a cube is 5.6 cm. What is the volume of the largest sphere that can be taken out of the cube?
If sec 2θ = cosec (θ – 36°), where 2θ is an acute angle, find the value of θ.
What will be the value of sin 10° – 4/3 sin3 10°?
If the length of certain rectangle is decreased by 4 cm and breadth is increased by 2 c, it would result in a square of the same area. What is the perimete...
A wire is in the form of square with side 11 cm. It is bent to form a circle. What is the radius of the circle?
The mean proportional of a and b is c. What is the mean proportional of a2 c and b2 c?
The mid points of AB and AC of a ∆ABC are X and Y, respectively. If BC + XY = 24 units, then the value of BC − XY is:
Find the area of the sector of a circle with radius 4cm and angle 30°.
If b sin θ = a, then sec θ + tan θ = ?
The perimeter of a sector of a circle, whose radius is 20 cm, is 60 cm. If the length of a rectangle is 10 cm more than the arc subtended by the sector and...

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