Question 1

A room is 15 feet long and 12 feet broad. A mat has to be placed on the floor of the room leaving 1.5 feet space from the walls. What will be the cost of the mat at the rate of Rs. 3.50 per squire feet?

Accepted Answer

378

Question 2

Find the ratio of the areas of the incircle and circumcircle of a square ?

Accepted Answer

1 : 2

Question 3

The perimeter of a rectangle whose length is 6 m more than its breadth is 84 m. What will be the area of the rectangle?

Accepted Answer

Let the breadth of the rectangle = b mts Then Length of the rectangle = b + 6 mts Given perimeter = 84 mts 2(L + B) = 84 mts 2(b+6 + b) = 84 2(2b + 6) = 84 4b + 12 = 84 4b = 84 - 12 4b = 72 b = 18 mts => Length = b + 6 = 18 + 6 = 24 mts Now, required Area of the rectangle = L x B = 24 x 18 = 432 sq. mts

Question 4

What is the least number of squares tiles required to pave the floor of a room 15.17 m long and 9.02 m broad?

Accepted Answer

Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm. Area of each tile = 41 × 41 c m 2 Required number of tiles = 1517 × 902 41 × 41 = 814

Question 5

A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 5 metres apart, how many poles will be needed?

Accepted Answer

Length of the wire fencing = perimeter = 2(90 + 50) = 280 metres Two poles will be kept 5 metres apart. Also remember that the poles will be placed along the perimeter of the rectangular plot, not in a single straight line which is very important. Hence number of poles required = 280 / 5 = 56

Question 6

The length and the breadth of rectangular field are in the ratio of 8 : 7. If charges of the painting the boundary of rectangle is at Rs. 10 per meter is Rs. 3000. What is the area of rectangular plot?

Accepted Answer

Perimeter of the rectangle is given by 3000/10 = 300 mts But we know, The Perimeter of the rectangle = 2(l + b) Now, 2(8x + 7x) = 300 30x = 300 x = 10 Required, Area of rectangle = 8x x 7x = 56 x 100 = 5600 sq. mts.

Question 7

If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.

Accepted Answer

Let x and y be the length and breadth of the rectangle respectively. Then, x - 4 = y + 3 or x - y = 7 ----(i) Area of the rectangle =xy; Area of the square = (x - 4) (y + 3) (x - 4) (y + 3) =xy <=> 3x - 4y = 12 ----(ii) Solving (i) and (ii), we get x = 16 and y = 9. Perimeter of the rectangle = 2 (x + y) = [2 (16 + 9)] cm = 50 cm.

Question 8

The no of revolutions a wheel of diameter 40cm makes in traveling a distance of 176m is

Accepted Answer

distance covered in 1 revolution = 2 πr = 2 x (22/7) x 20 = 880/7 cm required no of revolutions = 17600 x (7/880) = 140

Question 9

A wheel makes 1000 revolutions in covering a distance of 88 km. Find the radius of the wheel.

Accepted Answer

Distance covered in one revolution = 88 × 1000 1000 = 88m. 2 πR 2 = 88 ⇒ 2 × 22 7 × R = 88 ⇒ R = 88 × 7 44

Question 10

A circular swimming pool is surrounded by a concrete wall 4ft wide. If the area of the concrete wall surrounding the pool is 11/25 that of the pool, then the radius of the pool is?

Accepted Answer

let the radius of the pool be Rft Radius of the pool including the wall = (R+4)ft Area of the concrete wall = π R + 4 2 - R 2 = π R + 4 + R R + 4 - R = 8 π R + 2 sq feet => 8 π R + 2 = 11 25 πR 2 = > 11 R 2 = 200 R + 2 Radius of the pool R = 20ft

Question 11

The breadth of a rectangular field is 60% of its length. If the perimeter of the field is 800 m.What is the area of the field?

Accepted Answer

Let length = x meters, then breadth = 0.6x Given that perimeter = 800 meters => 2[ x + 0.6x] = 800 => x = 250 m Length = 250m and breadth = 0.6 x 250 = 150m Area = 250 x 150 = 37500 sq.m

Question 12

A typist uses a sheet measuring 20cm by 30cm lengthwise.If a margin of 2 cm is left on each side and a 3 cm margin on top and bottom, then percent of the page used for typing is

Accepted Answer

Area of the sheet = 20 × 30 c m 2 Area used for typing = 20 - 4 × 30 - 6 c m 2 required % = 384 600 × 100 =64%

Question 13

The difference between circumference and semidiameter of a circle is 37 cm. What is the diameter of the circle ?

Accepted Answer

circumference of a circle = 2 π r => 2 × 22/7 × r – r = 37 => 37/7 × r = 37 => r = 7 cm. Diameter D = 2r = 7×2 = 14 cm.

Question 14

If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area ?

Accepted Answer

The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm. Area of the triangle =1/2 x base x height => 1/2 x 24 x 10 = 120 sq.cm

Question 15

Find the area of the square whose side is equal to the diagonal of a rectangle of length 3 cm and breadth 4 cm.

Accepted Answer

Given length of the rectangle = 3 cm Breadth of the rectangle = 4 cm Then, the diagonal of the rectangle D = 3 2 + 4 2 = 25 = 5 Then, it implies side of square = 5 cm We know that Area of square = S x S = 5 x 5 = 25 sq.cm.

Question 16

A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required?

Accepted Answer

Given that length and area, so we can find the breadth. Length x Breadth = Area => 20 x Breadth = 680 => Breadth = 34 feet Area to be fenced = 2B + L = 2 (34) + 20 = 88 feet

Question 17

The breadth of a rectangular field is 75% of its length. If perimeter of the field is 1050 m, what will be th area of field ?

Accepted Answer

Let the length be 'l' and breadth be 'b'. b = l × 3/4__________(a) 2(l+b) = 1050 l+b = 525___________(b) From equations (a) and (b), l = 300m, b = 225 m Area = l × b = 300 × 225 = 67500 sq.m.

Question 18

The length, breadth and height of a room are in the ratio 7:3:1. If the breadth and height are doubled while the length is halved, then by what percent the total area of the 4 walls of the room will be increased ?

Accepted Answer

Let length, breadth and height of the room be 7, 3, 1 unit respectively. Area of walls = 2(l+b)xh = 2(7+3)x1 = 20 sq. unit. Now, length, breadth and height of room will become 3.5, 6 and 2 respectively. Area of walls = 2(l+b)xh = 2(3.5+6)x2 = 38 sq. unit. % Increase in the area of walls = (38-20)x100/20 = 90%.

Question 19

How many square units in 13 by 9?

Accepted Answer

Number of square units in 13 by 9 is given by the area it forms with length and breadth as 13 & 9 Area = 13 x 9 = 117 Hence, number of square units in 13 by 9 is 117 sq.units.

Question 20

Find the area of a square, one of whose diagonals is 3.8 m long

Accepted Answer

Area of the square = 1 2 * d i a g o n a l 2 = 1 2 * 3 . 8 * 3 . 8 = 7 . 22 m 2

Area Questions