Cylinder and Cuboid Questions for NMAT – Download [PDF]

Download Cylinder and Cuboid Questions for NMAT PDF. Top 10 very important Cylinder and Cuboid Questions for NMAT based on asked questions in previous exam papers.

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Question 1: An ant starts crawling at the bottom of a right circular cylinder and reaches the top of the cylinder on the diametrically opposite side along the shortest path. What is the distance covered by the ant if the height of the cylinder is 30 cm and the circumference of the base is 80 cm?

a) 55 cm

b) 30 cm

c) 40 cm

d) 50 cm

Question 2: An ant starts at one point on the circumference of the base of a cylinder of base radius = 14 cm and height = 66 cm and crawls to the corresponding point on the other end of the cylinder along a spiral path on the curved surface area of the cylinder. What is the length of the shortest path that the ant can take? ( $\pi = 22/7$ )

a) 110 cm

b) 94 cm

c) 100 cm

d) 120 cm

Question 3: The cost of a cylinder is directly proportional to its height and inversely proportional to its base area. Find the ratio of the prices of the two cylinders whose heights are in the ratio 3:4 and whose base radii are in the ratio 4:3?

a) 4:3

b) 64:27

c) 9:16

d) 27:64

Question 4: A cylinder of radius 12 cm was filled to the brim. A sphere of radius 3 cm was completely immersed into the cylinder and removed out. By how much has the height of water gone down in the cylinder?

a) 1 cm

b) 0.5 cm

c) 0.25 cm

d) None of these

Question 5: A cuboid dimensions 10x11x12 is cut into unit cubes and then painted with red colour. Find the number of unit cubes that have 0 faces painted?

a) 990

b) 1320

c) 0

d) None of the above

Question 6: A painted cuboid of dimensions 5x6x7 is cut into unit cubes. What is the number of unit cubes that have 0 faces painted?

a) 50

b) 60

c) 40

d) 210

Question 7: A cuboid has dimensions length 4m, width 3m and height 1m. A shearing force is applied on the top of a cuboid along the length of the cuboid such that it becomes a parallelepiped whose slant height is 2m. If the angle made by the slant surface with the base is 30º then what is the % change in total surface area?

a) 15.78% increase in area

b) 15.78% decrease in area

c) 7.84% increase in area

d) 7.84% decrease in area

Question 8: A cuboid of dimensions 10X11X12 is painted on all its faces. The cuboid is then entirely cut into smaller cubes of unit volume. Find the number of such unit cubes which have paint on exactly two of their faces.

a) 216

b) 108

c) 724

d) 484

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Answers & Solutions:

1) Answer (D)

If the cylinder is cut along its height to form a rectangle of dimensions 80 cm X 30 cm, the line joining one vertex to the midpoint of the opposite side is along which the ant has traveled.

Path travelled by the ant is the dotted line AE.

Length = $\sqrt{40^2+30^2}=50$ cm

2) Answer (A)

Imagine the cylinder to be cut across AD in such a way that it forms a rectangle with sides 2*(22/7)*14 = 88 cm and 66 cm. The required path is the diagonal of the rectangle = 110 cm.

3) Answer (D)

The ratio of base areas is 16:9. So, ratio of the prices is 3/4*9/16 = 27/64

4) Answer (C)

3.14 * 12 * 12 * h = 4/3 * 3.14 * 3 * 3 * 3
So, h = 0.25 cm

5) Answer (C)

Since the cubes are painted after the 10x11x12 cuboid is cut, all the unit cubes will have their all faces covered with paint.

So, there will be no cube that will have none of its faces covered by paint.

6) Answer (B)

The number of unit cubes that have no face painted = number of unit cubes that are hidden = (5-2)*(6-2)*(7-2) = 3*4*5 = 60

7) Answer (A)

TSA before the force was applied = 2(3*4 + 4*1+3*1) = 38 sq m

After the force is applied, the cuboid becomes a parallelopiped with a slant height of 2m and angle of slant surface is 30º.

Thus, the height h = 2 sin 30 = 1m

So the surfaces will be 2 parallelograms with bases 4m and height 1m, 2 rectangles with sides 3m and 2m and 2 rectangles with sides 3m and 4m.

TSA = 2*(4*1)+2*(3*2)+2*(3*4) = 2*22 = 44 sq m

% Change in area = (44-38) / 38 = 15.78% increase in area

8) Answer (B)

The unit cubes with paint on exactly 2 faces reside on the edges of the cuboid. The cuboid has 12 edges. There are 4 edges of length 12, 4 edges of length 11 and 4 edges of length 10. On the edge with length 12 unit cubes, the number of cubes which have exactly 2 faces covered by paint = 12-2 = 10. Similarly, on the edge with 11 unit cubes, the number of cubes covered by paint on exactly 2 faces = 11-2 = 9. The number of cubes with exactly 2 faces covered by paint on the 10 unit cube edge is 10-2 = 8. Therefore, the total number of unit cubes which have exactly 2 faces covered by paint = 4*(10+9+8) = 4*27 = 108.

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