#QuAnTuMMCQs , #CAT , #QUANT , #Mensuration.
1️⃣ A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:
A)12cm3
B)15cm3
C)16cm3
D) 20cm3
2️⃣ In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
A)75 cu. m
B)750 cu. m
C)7500 cu. m
D)75000 cu. m
3️⃣ A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
A)720
B)900
C)1200
D)1800
4️⃣ 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:
A)84
B)90
C)168
D)336
5️⃣ A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:
A)3.6 kg
B)3.696 kg
C)36 kg
D)36.9 kg
6️⃣ A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
A)12 kg
B)60 kg
C)72 kg
D)96 kg
7️⃣ 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:
A)20 cm
B)25 cm
C)35 cm
D)50 cm
8️⃣ The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.
A)30m2
B)40m2
C)60m2
D)80m2
9️⃣ A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
A)49 m2
B)50 m2
C)53.5 m2
D)55 m2
A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:
A)4830
B)5120
C)6420
D)8960
Answers
Answer:
Step-by-step explanation:
Question 1:
Volume of cone = 1/3 π r² h = 1/3*22/7*3*3*4 = 12 π cm³
Question 2:
1 hectare = 10,000 m²
Area = (1.5 x 10000) m²= 15000 m²
Depth = 5/100 m= 1/20 m
Volume = (Area x Depth)
=15000 x 1/20 m³
= 750 m³
Question 3:
2(15 + 12) x h = 2(15 x 12)
h =180/27 m = 20/3 m
Volume = 15 x 12 x 20/3 m³ = 1200 m³
Question 4:
Let the length of the wire be h.
Radius = 1/2 mm =1/20 cm
Then, Volume = π r² h
22/7*(1/20)²h = 66
h =66 x 20 x 20 x 7/22 = 8400 cm = 84 m.
Question 5:
External radius = 4 cm, Internal radius = 3 cm.
Volume of iron = 22/7 x [(4)² - (3)²] x 21 cm³
=22/7 x 7 x 1 x 21 cm ³
= 462 cm³.
Weight of iron = (462 x 8) gm = 3696 gm = 3.696 kg.
Question 6:
Volume of water displaced = 3*2*0.01 = 0.06 m cube
Mass of Man = Volume of water displaced * Density of water
= 0.06 * 1000 = 60 kg
Question 7:
Total volume of water displaced = (4 x 50) m³ = 200 m³.
Rise in water level = (200*20/40) * 0.25 = 25 cm.
Question 8:
l=10 m
h=8 m
r = √[l² – h²] = √[(10)² – (8)²] = 6 m
Curved surface area = 22/7 * 6 * 10 = 60πm²
Question 9:
The wet surface will be: the base 6*4 =24 m² + 2 walls of 1.25*4 = 10 m² + two walls of 1.25* 6 = 15 m²
Thus total = 24 + 10 + 15 =49 m²
Question 10:
l = (48 - 16)m = 32 m, [because 8+8 = 16]
b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (32 x 20 x 8)
= 5120 m³