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

**1. Cuboid volume and Base area are 144 m ^{3} and 18 m^{3}respectively. Find the height of a cuboid?**

Answer: 8 metre

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?
Answer: 20
Explanation:
Breadth = x metres.
Length = ( 115x / 100 ) metres
⇒ x * ( 115x / 100 ) = 460
115x**

^{2}= ( 460 * 100 ) 115x

^{2}= ( 460 * 100 ) / 115 x

^{2}= 400 x = 20

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

**4. What is area? If the circumference of a circle is 22 cm.
Answer: 38.5 cm ^{2}
Explanation:
Circumference = 22 cm
22 = 2 * ( 22 / 7 ) * r
r = ( 7 / 2 ) cm
Area of circle = Πr^{2}
= ( 22 / 7 ) * ( 7 / 2 )^{2}
= 38.5 cm^{2}**

**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?
Answer: 200 miles
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 cm ^{2}. What is its circumference?
Answer: 44 cm
Explanation:
Area = 154
Π r^{2} = 154
( 22 / 7 ) * r^{2} = 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?
Answer: 45 km
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?
Answer: 14 m
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?
Answer: 81
Explanation:
90**

^{2}< 8200 < 91

^{2}⇒ 8100 < 8200 < 8281 ∴ Required number = 8281 – 8200 = 81

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

**11. Find the greatest possible length which can be used to measure exactly the lengths 4m 95cm, 9m, 16m 65cm?
Answer: 45 cm
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 = 3**

^{2}* 5 * 11 ∴ 900 = 2

^{2}* 3

^{2}* 5

^{2}∴ 1665 = 3

^{2}* 5 * 37 H.C.F = 3

^{2}* 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?
Answer: 56 m
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?
Answer: 4913 cm ^{3}
Explanation:
Let the edge of the cube be a.
6a^{2} = 1734
a^{2} = 1734 / 6
a^{2} = 289
a = 17 cm
Volume = a^{3}
= ( 17 )^{3} cm^{3}
= 4913 cm^{3}**

**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?
Answer: Rs. 1934.40
Explanation:
Area of the carpet = Area of the room
= ( 13 * 9 ) m**

^{2}= 117 m

^{2}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?
Answer: Rs. 16500
Explanation:
Area of the floor = ( 5.5 * 3. 75 ) m**

^{2}= 20.625 m

^{2}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 ?
Answer: 49
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?
Answer: 84 m
Explanation:
Let inner radius be r meters
Outer 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?
Answer: 75 %
Explanation:
Let original radius = R
New radius = ( 50 / 100 ) * R
= ( R / 2 )
Original area= πR**

^{2}New area= π( R / 2 )

^{2}= πR

^{2}/ 4 Decrease in area = ( 3πR

^{2}/ 4 ) * ( 1 / πR

^{2}) * 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?
Answer: 400 m ^{2}
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 m^{2}**

**20. Find the area, in hectare, of a field whose length is 240 m and width 110 m?
Answer: 2.64 hectare
Explanation:
Length l = 240 m
Width w = 110 m
Area of the field = l * w
= 240 * 110
= 26400 m**

^{2}Area of field = 26,400 / 10000 ( ∴ 10000 m

^{2}= 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?
Answer: 200 m
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?
Answer: 1176 cm ^{2}
Explanation:
Volume of a cube a^{3} = 2744
a^{3} = ( 14 )^{3}
a = 14
Surface area = 6a^{2}
= 6 * ( 14 )^{2}
= 6 * 196
= 1176 cm^{2}**

**23. Find the value of ( 99 ) ^{2}
Answer: 9801
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?
Answer: 24 a ^{2}
Explanation:
Edge of a cube = 2a cm
Surface = 6a^{2}
= 6 * ( 2a ) * ( 2a )
= 6 * ( 4a^{2} )
= 24 a^{2}**

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

Answer: 120000

Explanation:

Capacity = Volume of tank ( ∴ 1m = 100cm )

= [ ( 8 * 100 ) * ( 6 * 100 ) * ( 2.5 * 100 ) ] / 1000

= ( 800 * 600 * 250 ) / 1000

= 80 * 60 * 25

= 120000