# [sg_popup id=”1345″ event=”inherit”][/sg_popup]Area related Problems

1. Cuboid volume and Base area are 144 m3 and 18 m3respectively. Find the height of a cuboid?
Explanation:
Height of the cuboid = ( Volume / Base area )
= 144 / 18
= 8 metre

2. The area of a rectangle is 460 square metres. If the length is 15% more than the breadth. What is the breadth of the rectangular field?
Explanation:
Length = ( 115x / 100 ) metres
⇒ x * ( 115x / 100 ) = 460
115x2 = ( 460 * 100 )
115x2 = ( 460 * 100 ) / 115
x2 = 400
x = 20

3. The area of a parallelogram is 72 cm2and its altitude is twice the corresponding base. What is the length of the base?
Explanation:
Let the base = x cm.
Height = 2x cm (∴ altitude is twice the base)
Area = b * h
= x * 2x
= 2x2
The area is given = 72 cm2
⇒ 2x2 = 72
x2 = 36
x = 6 cm

4. What is area? If the circumference of a circle is 22 cm.
Explanation:
Circumference = 22 cm
22 = 2 * ( 22 / 7 ) * r
r = ( 7 / 2 ) cm
Area of circle = Πr2
= ( 22 / 7 ) * ( 7 / 2 )2
= 38.5 cm2

5. River A and River B have a combined length of 650 miles and River B is 250 miles shorter than River A. How many miles long is River B?
Explanation:
Total length of River A and River B is 650 miles
Let x be the length of River A.
River B is 250 miles shorter than River A.
Hence length of River B is x – 250.
∴ x + x – 250 = 650
2x = 650 + 250
x = 900 / 2
= 450
Length of River A = 450 miles
Length of River B = 450 – 250
= 200 miles

6. The area of circle is 154 cm2. What is its circumference?
Explanation:
Area = 154
Π r2 = 154
( 22 / 7 ) * r2 = 154
r = 7 cm
Circumference = 2Πr
= 2 * ( 22 / 7 ) * 7
= 44 cm

7. A student comes from school partly by foot at 5 kmph and by bicycle at 8 kmph. The distance covered by him is 51 km in 9 hours. Find the distance travelled on foot?
Explanation:
Distance covered on foot = x km
Distance covered on bicycle = 51 – x
∴ ( x / 5) + [ ( 51 – x ) / 8 ] = 9
( 8x + 225 – 5x ) / 40 = 9
3x = 360 – 225
3x = 135
⇒ x = 45 km

8. A wheel makes 1000 revolutions in covering a distance of 88 km. Find the radius of the wheel?
Explanation:
Distance covered in one revoluti 88 * 1000 ) / 1000
= 88 m
Distance ⇒ 2ΠR = 88
2 * ( 22 /7 ) * R = 88
R = 88 * ( 7 / 44 )
= 14 m

9. What is the least number to be added to 8200 to make it a perfect square?
Explanation:
902 < 8200 < 912
⇒ 8100 < 8200 < 8281
∴ Required number = 8281 – 8200
= 81

10. Find the surface area of a 10 cm, 4cm, 3cm brick?
Explanation:
Surface area = 2 ( lb * bh * lh )sq. units
= [ 2 * ( ( 10 * 4) + ( 4 * 3 ) + ( 10 * 3 ) ) ] cm2
= [ 2 * ( 40 + 12 + 30) ] cm2
= [ 2 * 82 ] cm2
= 164 cm2

11. Find the greatest possible length which can be used to measure exactly the lengths 4m 95cm, 9m, 16m 65cm?
Explanation:
Required length = H.C.F of 4m 95cm, 9m and 16m 65cm. ( ∴ 1 metre = 100 cm )
= H.C.F of 495cm, 900cm, 1665cm.
∴ 495 = 32 * 5 * 11
∴ 900 = 22 * 32 * 52
∴ 1665 = 32 * 5 * 37
H.C.F = 32 * 5
= 45cm
Hence, required length = 45 cm

12. 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?
Explanation:
Perimeter of the polt = 2 * ( 90 + 50 )
= 2 * ( 140 )
= 280
Number of poles = ( 280 / 5 )
= 56 m

13. The surface area of a cube is 1734 sq.cm. Find its volume?
Explanation:
Let the edge of the cube be a.
6a2 = 1734
a2 = 1734 / 6
a2 = 289
a = 17 cm
Volume = a3
= ( 17 )3 cm3
= 4913 cm3

14. Find the cost of carpeting a room 13m long and 9m broad with a carpet 75cm wide at the tate of Rs. 12.40 per square metre?
Explanation:
Area of the carpet = Area of the room
= ( 13 * 9 ) m2
= 117 m2
Length of the carpet = area / width
= [ 117 * ( 4 / 3 ) ] m
= ( 39 * 4 ) m
= 156 m
Cost of carpeting = Rs. ( 156 * 12.40 )
= Rs. 1934.40

15. The length of the room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 800 per sq. metre?
Explanation:
Area of the floor = ( 5.5 * 3. 75 ) m2
= 20.625 m2
Cost of paving = Rs. ( 800 * 20.625 )
= Rs. 16500

16. A rope makes 70 rounds of the circumference of a cylinder whose radius of the base is 14 cm. How many times can it go round a cylinder with radius 20 cm ?
Explanation:
Let the required number of round be x.
⇒ More radius, Less rounds. ( ∴ Indirect proportion )
⇒ 20 : 14 :: 70 : x
⇒ 20 * x = 14 * 70
x = ( 14 * 70 ) / 20
x = 7 * 7
x = 49
Hence, the required number of rounds = 49

17. The inner circumference of a circular race track, 14 m wide is 440 m. Find the radius of the outer circle?
Explanation:
Let inner radius be r meters
Then, 2πr = 440
2 * ( 22 / 7 ) * r = 440
r = 440 * ( 7 / 44 )
= 10 * 7
r = 70 m
R – r = 14 m
R = 14 m + 70 m
Radius of outer circle = ( 14 m + 70 m ) m
= 84 m.

18. If the radius of a circle is decreased by 50%, find the percentage decrease in its area?
Explanation:
New radius = ( 50 / 100 ) * R
= ( R / 2 )
Original area= πR2
New area= π( R / 2 )2
= πR2 / 4
Decrease in area = ( 3πR2 / 4 ) * ( 1 / πR2 ) * 100
= ( 3 / 4 ) * 100
= 300 / 4
= 75 %

19. A field is 40 metre long and 35 metre wide. The field is surrounded by a path of uniform width of 2.5 metre runs round it on the outside. Find the area of the path?
Explanation:
Remember the formula for the Area of path = 2 * Width * [ Length + Breadth + ( 2 * Width ) ]
= 2 * 2.5 * [ 40 + 35 + ( 2 * 2.5 ) ]
= 5 * ( 75 + 5 )
= 5 * ( 80 )
= 400 m2

20. Find the area, in hectare, of a field whose length is 240 m and width 110 m?
Explanation:
Length l = 240 m
Width w = 110 m
Area of the field = l * w
= 240 * 110
= 26400 m2
Area of field = 26,400 / 10000 ( ∴ 10000 m2 = 1 hectares )
= 2.64 hectare

21. The length of a rectangular field is twice its width. A man jogged around it 5 times and covered a distance of 3 km. What is the length of the field?
Explanation:
In completing one round of the field distance covered is equal to the perimeter of the field.
Distance covered in 5 rounds = 5 * Perimeter
= 5 * [ 2 ( l + w ) ]
= 5 * 2 ( l + w )
= 10 * ( l + w )
= 10 * ( 2w + w ) ( ∴ length l = 2w )
= 10 * 3w
= 30 w
The total distance covered is given = 3 km ( ∴ 1 km = 1000 m )
= 3000 m
⇒ ( 30 * w ) = 3000
w = 3000 / 30
w = 100 m
Length = 2 w
= ( 2 * 100 ) m
= 200 m

22. The volume of a cube is 2744 cube.cm, find its surface area?
Explanation:
Volume of a cube a3 = 2744
a3 = ( 14 )3
a = 14
Surface area = 6a2
= 6 * ( 14 )2
= 6 * 196
= 1176 cm2

23. Find the value of ( 99 )2
Explanation:
( 99 )2 = ( 100 – 1 )2
= ( 100 )2 – 2 * 100 * 1 + ( 1 )2
= 10000 – 200 + 1
= 9800 + 1
= 9801

24. The edge of a cube is 2a cm. Find its surface?
Explanation:
Edge of a cube = 2a cm
Surface = 6a2
= 6 * ( 2a ) * ( 2a )
= 6 * ( 4a2 )
= 24 a2

25. Find the capacity of a tank of dimensions ( 8 m * 6 m * 2.5 m ) ?