Q1. A semi-circle has perimeter 36. What will be the area of complete circle?
(a) π(36/(π + 2))^2
(b) π(36/(π – 2))^2
(c) π^2 (36/(π + 2))^2
(d) π(36/(π – 2))^2
Sol.
πr+2r=30
r=30/(π + 2)
⇒ Area =π〖30/(π + 2)〗^2
Q2. A rectangle is made of wire having length 17 cm & breadth 7 cm. Then rectangle is unfold and made a square. Which will have more area and how much?
(a) Rectangle, 25 cm2
(b) Square 23 cm2
(c) Square, 25 cm2
(d) Rectangle, 23 cm2
Sol.
Area of rectangle =17×7=119 cm^2
Perimeter of rectangle = 2(17 + 7) = 48 cm
Side of square =48/4=12 cm
Area of square =(12)^2=144 cm^2
Area of square is 25 cm2 more than rectangle
Q3. The perimeter of equilateral triangle is 12 cm. What will be its area?
(a) 4√2 cm^3
(b) 4√3 cm^2
(c) 5 √3 cm^3
(d) 3√2 cm^2
Sol.
3x = 12
x = 14
Area =√3/4 x^2
=√3/4 (4)^2=4√3
Q4. A rectangle filed has area equal to 150 m2 and perimeter 50 m. Its length and breadth respectively must be
(a) 30 m, 5 m
(b) 25 m, 6 m
(c) 15 m, 10 m
(d) None of the above
Sol.
l × b = 150
and 2(l + b) = 50 ⇒ l + b = 25
Clearly l = 15, b = 10
Q5. The lateral surface area and total surface area of cylinder is 616 cm2 and 924 cm2 respectively. What will be its volume?
(a) 2156 cm3
(b) 2155 cm3
(c) 2145 cm3
(d) 2165 cm3
Sol.
2πrh=616 …(i)
2πr(h+4)=924 …(ii)
2πrh/2πr(h +r) =616/924
924h = 616h + 616r
308h = 616r
h = 2r
Putting value in (i)
2πr×2r=616
r^2=(616 × 7)/(4 × 22)=49
r = 7
h =(616 × 7)/(2 × 22 × 7)=14
Volume =πr^2 h
=22/7×7×7×14
= 2156 cm3
Q6. A circle has area which is 100 times the area of another circle. The ratio of their circumferences is
(a) 1 : 10
(b) 100 : 1
(c) 10 : 1
(d) None of the above
Sol.
A1=100A2
⇒ 〖πr1〗^2 = 100〖πr〗^2
⇒ 〖r1〗^2=100〖r2〗^2
⇒ r1/r2 =10/1
C1/C2 =(2πr1)/〖2πr2〗 =r1/r2 =10/1
⇒ C1 ∶ C2=10∶1
Q7. Four equal circles of radius 7 cm touch each other as shown in figure. The area of the shaded part is
(a) 84 cm2
(b) 21 cm2
(c) 42 cm2
(d) None of the above
Sol.
Join centers to obtain a square of side 14 cm.
Q8. If each side of a rectangle is increased by 50%, its area will increase by
(a) 125%
(b) 75%
(c) 100%
(d) 225%
Sol.
Original area = l × b
New area =3/2 l×3/2 b=9/4 lb
Increase % =(9/4 lb – lb)/lb×100%
= 125%
Q9. Diagonals of a rhombus are in the ratio 3 : 4 and its area is 2400 cm2. Side of the rhombus is
(a) 20 cm
(b) 40 cm
(c) 50 cm
(d) 100 cm
Sol.
d1=3x, d2=4x
1/2× 3x × 4x=2400
⇒ x^2=400⇒x=20
Use : Side =1/2 √(d1^2+d2^2 )
Q10. The breadth of rectangle filed is 60 per cent of its length. If the perimeter of filed is 800 metres then, what is area of the filed?
(a) 37,500 m2
(b) 48,00 m2
(c) 18,750 m2
(d) 40,000m
Sol.
Let length = 1
∴ breadth =60/100 l= 3/5 l
2(l + b) = 800
2(l+3/5 l)=800
16/5 l=800
l = 250 m
Area = l × b
=250×3/5×250
= 37500 m2
