Question 1

The edge of three cubes of metal is 3 m, 4 m and 5 m. They are melted and formed into a single cube. Find the edge of the new cube ?

Accepted Answer

The edge of the new cube is = 3 3 + 4 3 + 5 3 = a 3 => a = 6 m.

Question 2

A class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the class room ?

Accepted Answer

Length = 6 m 24 cm = 624 cm Width = 4 m 32 cm = 432 cm HCF of 624 and 432 = 48 Number of square tiles required = (624 x 432)/(48 x 48) = 13 x 9 = 117.

Question 3

Calculate the number of bricks, each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 cm x 6 m when 10% of its volume is occupied by mortar ?

Accepted Answer

Let the number of bricks be 'N' 10 x 4/100 x 6 x 90/100 = 25/100 x 15/100 x 8/100 x N 10 x 4 x 6 x 90 = 15 x 2 x N => N = 720.

Question 4

Chord AB of a circle when extended meets the tangent to the circle at point P. PT is the tangent touching the circle at point T. If lengths of PT and PB are 6 cm and 4 cm respectively, what is the length of PA?

Accepted Answer

9 cm

Question 5

Two concentric circles form a ring. The inner and outer circumference of the ring are 352/7 m and 528/7m respectively.Find the width of the ring.

Accepted Answer

let the inner and outer radii be r and R meters then, 2 πr = 352/7 => r = (352/7) * (7/22) * (1/2) = 8m 2 πR = 528/7 => R= (528/7) * (7/22) * (1/2)= 12m width of the ring = R-r = 12-8 = 4m

Question 6

The perimeters of two squares are 40cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.

Accepted Answer

side of first square = 40/4 =10cm side of second square = 32/4 = 8cm area of third squre = 10² - 8² = 36 sq cm side of third square = 36 = 6 cm required perimeter = 6*4 = 24cm

Question 7

A cow s tethered in the middle of a field with a 14feet long rope.If the cow grazes 100 sq feet per day, then approximately what time will be taken by the cow to graze the whole field?

Accepted Answer

area of the field grazed = (22/7) * 14 * 14 = 616 sq feet

Question 8

Wheels of diameters 7cm and 14cm start rolling simultaneously from x & y which are 1980 cm apart towards each other in opposite directions. Both of them make the same number of revolutions per second. If both of them meet after 10seconds.The speed o…

Accepted Answer

let each wheel make x revolutions per sec. Then 2 π * 7 2 * x + 2 π * 7 * x * 10 = 1980 2 * 22 7 * 7 2 * x + 2 * 22 7 * 7 2 * x = 198 66 x = 198 distance moved by smaller wheel in 3 revolutions = 2 * 22 7 * 7 2 * 3 = 66 c m speed of smaller wheel = 66 3 m/s = 22m/s

Question 9

The length of the rectangle is 20% more than its breadth . what will be the ratio of the area of the rectangle to that of the square whose side is equal to the breadth of the rectangle?

Accepted Answer

Required ratio = 6 x 5 × x × 1 x 2 = 6 : 5

Question 10

The perimeter of a square is equal to twice the perimeter of a rectangle of length 8cm and breadth 7cm. What is the circumference of a semicircle whose diameter is equal to the side of the square ?

Accepted Answer

We know that perimeter of rectangle = 2(l+b) = 2(8+7)= 30cm Given perimeter of square is twice the perimeter of rectangle = 2(30) = 60cm Therefore, side of the square is = 1/4 x 60 = 15cm Circumference of the required semicircle = πr + 2 r = 22 7 × 15 2 + 2 × 15 2 = 23.57 + 15 = 38.57cm.

Question 11

If a 36 cm thread is used to wrap a book, lengthwise twice and breadth wise once, what is the size of the book ?

Accepted Answer

Length of the thread is 36 cms. length wise twice breath wise once then totally thrice. so 36/3 = 12. so length is 12 x 2 = 24 cms breath is 12 cms Area of the book = length x breath = 24 x 12 = 288 sq.cm

Question 12

Let A(O,-1), B(0,3) and C(2,1) be three points. Let △1 be the area of the triangle ABC and △2 be the area of the triangle formed by the mid points of the sides of the triangle whose vertices are A, B and C such that △1 =1 , △2=x Find the value of x .

Accepted Answer

3

Question 13

A man walking at the speed of 4 kmph crosses a square field diagonally in 3 meters.The area of the field is

Accepted Answer

speed of the man = 4 x (5/18) m/sec = 10/9 m/sec time taken = 3 x 60 sec = 180 sec length of diagonal = speed x time = (10/9) x 180 = 200m Area of the field = (1/2) x (dioagonal)² = (1/2) x 200 x 200 sq.m = 20000sq.m

Question 14

The length of a rectangular plot is 20 meters more than its breadth. If the cost of fencing the plot @ 26.50 per meter is Rs. 5300. What is the length of the plot in meter?

Accepted Answer

let breadth = x then length = x+20 perimeter = 5300/26.50 = 200m 2(x+20+x) =200 => 4x+40 =200 x = 40 and length = 40+20 = 60m

Question 15

If the ratio of two squares is 225:256,then the ratio of the perimeters is

Accepted Answer

a 2 b 2 = 225 / 256

Question 16

The area of a square is 1024 sq.cm. What is the ratio of the length to the breadth of a rectangle whose length is twice the side of the square and breadth is 12 cm less than the side of this square ?

Accepted Answer

Area of a square SxS = 1024 => S = 32 cm Length of the rectangle = 32x2 cm = 64 cm Breadth of the rectangle = 32 - 12 = 20 cm Required ratio = 64 : 20 = 16 : 5

Question 17

A rectangular grassy plot 120 m. by 60 m has a gravel path 1.5 m wide all round it on the inside. Find the cost of gravelling the path at 65 paise per sq. metre ?

Accepted Answer

area of the plot = 120m x 60m = 7200 sq.m area of plot excluding gravel = 117m x 57m = 6669 sq.m area of gravel = 7200 sq.m - 6669 sq.m = 531 sq.m cost of building it = 531 sq.m x 65 ps = 34515 ps In Rs. = 34515/100 = Rs. 345.15.

Question 18

The perimeter of an isosceles triangle is 32 cm and each of the equal sides is 5/6 times of the base. What is the area (in cm2 ) of the triangle ?

Accepted Answer

48

Question 19

The lengths of diagonals of a rhombus are 24cm and 10cm the perimeter of the rhombus (in cm ) is :

Accepted Answer

52

Question 20

The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:

Accepted Answer

Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m.Area = (480 x 320) sq.m = 153600 sq.m

Area Questions