Surface Areas and Volume - Aptitude Questions and Answers | Online Surface Areas and Volume MCQ Aptitude Test
Quiz Name
Surface Areas and Volume
Category
Online Aptitude Test
Number of Questions
20
Time
30 Minutes
Exam Type
MCQ (Multiple Choice Questions)
1. To make a cone, spin a right triangle with sides of 3 cm, 4 cm, and 5 cm by 3 cm. The volume of the resulting cone is:
a. 12 cm3
b. 15 cm3
c. 16 cm3
d. 20 cm3
Answer: A
Explanation:
We can see that r = 3 cm and h = 4 cm.Volume = 1/3 x 32 x 4 cm3 = 12 cm3 Volume = 1 /3r2h = 1/3 x 32 x 4 cm3 = 12 cm3.
2. Five centimetres of rain fall during a shower. The amount of water that falls on 1.5 hectares of land is calculated as follows:
a. 75 cu. m
b. 750 cu. m
c. 7500 cu. m
d. 75000 cu. m
Answer: B
Explanation:
10,000 m2 Equals 1 hectare,As a result, the area equals (1.5 x 10000) m2 = 15000 m2.5/100 m = 1/20 m depth.15000 x 1/20 m3 = 750 m3 Volume = (Area x Depth).
3. A hall is 15 metres long and 12 metres wide. The volume of the hall is: if the total of the areas of the floor and ceiling equals the sum of the areas of the four walls.
a. 720
b. 900
c. 1200
d. 1800
Answer: C
Explanation:
2(15 + 12) =h = 180 / 27 m = 20/3 m,1200 m3 volume = 15 x 12 x 20/3 m3.
4. A wire with a diameter of 1 mm is produced from 66 cubic centimetres of silver. The wire's length in metres will be:
a. 84
b. 90
c. 168
d. 336
Answer: A
Explanation:
The wire's length should be h.1/20 cm = 1/2 mm radius.Then,66 = 22/7 x 1/20 x 1/20 x h,h = 8400 cm = 84 m = 66 x 20 x 20 x 7 /22 = 66 x 20 x 20 x 7 /22 .
5. A hollow iron pipe with an exterior diameter of 8 cm is 21 cm long. The weight of a pipe with a thickness of 1 cm and an iron density of 8 g/cm3 is:
a. 3.6 kg
b. 3.696 kg
c. 36 kg
d. 36.9 kg
Answer: B
Explanation:
4 cm external radius.3 cm internal radius.Iron volume = 22/7x [(4)2 - (3)2] x 21 cm3.7 x 1 x 21 cm3 = 22/7x 7 x 1 x 21 cm3,462 cm3 =(462 x 8) gramme = 3696 gm = 3.696 kg iron weight.
6. On a lake, a boat with a length of 3 metres and a width of 2 metres is floating. When a guy climbs on board, the boat sinks by 1 cm. The man's bulk consists of:
a. 12 kg
b. 60 kg
c. 72 kg
d. 96 kg
Answer: B
Explanation:
Volume of water displaced = 0.06 m3 (3 x 2 x 0.01) m3.The mass of a man is equal to the volume of water displaced multiplied by the density of water, which is (0.06 x 1000) kg = 60 kg.
7. On a religious day, 50 guys took a dip in a 40-meter-long, 20-meter-wide water tank. If a man's average water displacement is 4 m3, the rise in the water level in the tank will be:
a. 20 cm
b. 25 cm
c. 35 cm
d. 50 cm
Answer: B
Explanation:
4 × 50 m3 = 200 m3 total amount of water displaced.Water level rise = 200/40 x 20 m 0.25 m = 25 cm.
8. A right circular cone has a slant height of 10 m and a height of 8 m. Calculate the surface area of its curved surface.
a. 30 m2
b. 40 m2
c. 60 m2
d. 80 m2
Answer: C
Explanation:
l = 10 m,,,,,,,,,,,,,,,h = 8 metres,As a result, r = l2 - h2 = (10)2 - 82 = 6 metres.rl = ( x 6 x 10) m2 = 60 m2 Curved surface area.
9. A 6 m long by 4 m broad cistern holds water to a depth of 1 m 25 cm. The wet surface's entire area is:
a. 49 m2
b. 50 m2
c. 53.5 m2
d. 55 m2
10. A rectangular metallic sheet with dimensions of 48 m x 36 m is used. To produce an open box, a square is sliced off from each of its corners. If the square's length is 8 m, the box's volume (in m3) is:
a. 4830
b. 5120
c. 6420
d. 8960
Answer: B
Explanation:
Clearly, l = (48 - 16)m = 32 m, and l = (48 - 16)m = 32 m.(36 -16)m = 20 m, b = (36 -16)m =h = 8 metres=(32 × 20 x 8) m3 = 5120 m3 is the volume of the box.
11. A cylindrical pillar has a curved surface area of 264 m2 and a volume of 924 m3. Calculate the diameter to height ratio.
a. 3 : 7
b. 7 : 3
c. 6 : 7
d. 7 : 6
Answer: B
Explanation:
r2h/2rh = 924 /264 7 m = 924 x 2 /264 = 924 x 2 /264 = 924 x 2 /264 = 924 x 2 /264Furthermore, 2rh = 264 h = 264 x 7/22 x 1/2 x 1/7 = 6m.2r/h = 14/6 = 7:3 is the required ratio.
12. An 8000-litre cistern with exterior dimensions of 3.3 m by 2.6 m by 1.1 m and 5 cm thick walls. The bottom is of the following thickness:
a. 90 cm
b. 1 dm
c. 1 m
d. 1.1 cm
Answer: B
Explanation:
Allow for a thickness of x cm at the bottom.Then [(330 - 10) x (260 - 10) x (110 - x)] becomes [(330 - 10) x (260 - 10) x (110 - x)]. = 8000 x 1000 = 320 x 250 x (110 - x)=1 dm = x = 10 cm.
13. What is the total surface area of a right circular cone with a base radius of 7 cm and a height of 14 cm?
a. 344.35 cm2
b. 462 cm2
c. 498.35 cm2
d. None of these
Answer: C
Explanation:
r = 7 cm, h = 14 cm=As a result, l = (7)2 + (14)2 = 245 = 75 centimetres.=rl + r2 = 22/7 x 7 x 75 + 22/7 x 7 x 7 cm2 total surface area= [154(5 + 1) cm2 = 498.35 cm2 = (154 x 3.236) cm2.
14. From the material produced by melting three smaller cubes with sides of 3, 4, and 5 cm, a big cube is generated. What is the ratio of the smaller cubes' total surface areas to the giant cube's total surface area?
a. 2 : 1
b. 3 : 2
c. 25 : 18
d. 27 : 20
Answer: C
Explanation:
(33 + 43 + 53) = 216 cm3 is the volume of the big cube.Let the big cube's edge be a.As a result, a3 = 216 a = 6 cm.6 x (32 + 42 + 52)/6 x 62 = 50 /36= 25 : 18 is the required ratio.
15. How many 25 cm x 11.25 cm x 6 cm bricks will be required to construct an 8 m × 6 m x 22.5 cm wall?
a. 5600
b. 6000
c. 6400
d. 7200
Answer: C
Explanation:
Number of bricks = wall volume/brick volume = 800 x 600 x 22.5 / 25 x 11.25 x 6 = 6400.
16. The volume of a 32-meter-high cylindrical tank is what?
I. Its base covers an area of 154 m2.
II. The base has a 14-meter diameter.
a. I alone sufficient while II alone not sufficient to answer
b. II alone sufficient while I alone not sufficient to answer
c. Either I or II alone sufficient to answer
d. Both I and II are not sufficient to answer
Answer: C
Explanation:
Height is 32 metres.I offers a base area of 154 m2.(154 x 32) m3 = Volume = (Area of the base x Height).As a result, I am the only one who can provide an answer.According to II, the radius of the base is 7 metres.22/7 x 7 x 7 x 32 m3 = 4928 m3 =As a result, the solution may be found just in II.
17. Is a rectangular block considered a cube?
I. The rectangular block has at least two square faces.
II. The block has a volume of 64.
a. I alone sufficient while II alone not sufficient to answer
b.II alone sufficient while I alone not sufficient to answer
c. Either I or II alone sufficient to answer
d. Both I and II are not sufficient to answer
Answer: D
Explanation:
Any two of l, b, or h are equal, according to I.lbh = 64, according to II.The values of l, b, and h in I and II might be (1,1, 64), (2,2,16), and so on (4, 4, 4).As a result, the block might be a cube or a cuboid.
18. What is a cylindrical tank's capacity?
I. The base's radius is half of its height, which is 28 metres.
II. The base has a surface area of 616 square metres and a height of 28 metres.
a. I alone sufficient while II alone not sufficient to answer
b. II alone sufficient while I alone not sufficient to answer
c. Either I or II alone sufficient to answer
d. Both I and II are not sufficient to answer
Answer: C
Explanation:
h = 28 m and r = 14 are the results of I.Capacity = r2h may be calculated.As a result, I am the only one who can provide an answer.r2 = 616 m2 and h = 28 m are obtained from II.(r2 x h) = (616 x 28) m3 = capacityAs a result, the solution may be found just in II.
19. What is a circular cone's height?
I. That cone's area is the same as a 33-cm-long rectangle.
II. That cone's base measures 154 square centimetres.
a. I alone sufficient while II alone not sufficient to answer
b. II alone sufficient while I alone not sufficient to answer
c. Either I or II alone sufficient to answer
d. Both I and II are not sufficient to answer
Answer: D
Explanation:
r's value is given by II.However, the rectangle's width is not specified in I.As a result, we're unable to calculate the cone's surface area.As a result, it's impossible to estimate the cone's height.
20. How big is a cube's volume?
I. Each face of the cube has a surface area of 64 square metres.
II. One of the cube's sides is 8 metres long.
a. I alone sufficient while II alone not sufficient to answer
b. II alone sufficient while I alone not sufficient to answer
c. Either I or II alone sufficient to answer
d. Both I and II are not sufficient to answer
Answer: C
Explanation:
Allow a metre between each edge. Then,a2 = 64 a = 8 m a2 = 64 a2 = 64 a2 = 64 a2 = 64 a Volume = 512 m3 (8 x 8 x 8 m3).As a result, I am the only one who can provide an answer.a = 8 m a = 8 m a = 8 m a = 8 Volume = 512 m3 (8 x 8 x 8 m3).As a result, II alone provides the answer.
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