Practice Mensuration Questions and Answers

The value of tan2 θ + cot2 θ − sec2 θ cosec2 θ is:
The mean proportion of 169 and 144 is:
The circumference of the two circles is 198 cm and 352 cm respectively. What is the difference between their radii?
The length and breadth of a rectangle are increased by 8% and 5%, respectively. By how much percentage will the area of the rectangle increase?
Radius of a circle is 10 cm. Angle made by chord AB at the centre of this circle is 60 degree. What is the length of this chord?
In a right-angled triangle PQR, right-angled at Q, the length of the side PR is 17 units, length of the base QR is 8 units, and length of the side PQ is 15...
How many spherical lead shots each of diameter 8.4 cm can be obtained from a rectangular solid of lead with dimension 88 cm, 63cm, 42 cm(take π 22/7)?
If cot x – tan x = 3/2, then what will be the value of cot x + tan x?
If the diameter of a sphere is 63 cm, then what is the total surface area of the sphere?
On a rectangular wall of length 21 metres and height 18 metres, there is a window in the shape of triangle surmounted on a square. If the base of triangle ...
On a rectangular wall of length 22 metres and height 19 metres, there is a window in the shape of triangle surmounted on a square. If the base of triangle ...
In the election, 8% of the voters did not cast their votes. Two candidates contested the election in which the winning cadidate got 48% of the total votes ...
In the given figure, a circle is inscribed in Δ PQR, such that it touches the sides PQ, QR and RP at points D, E, F, respectively. If the lengths of the s...
Which of the following two will provide more volume? I) A cuboid of edges 6 cm, 7 cm and 8 cm II) A cube of edge 7 cm
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 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.
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?

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