Chapter 11: Mensuration

Solution: The correct answer is option (a) 6 cm

Explanation:

Given that, the metal sheet dimension is 27 cm long, 8 cm broad and 1 cm thick.

Thus, the volume of the sheet = (27)(8)(1) = 216 cm³

It is given that the metal sheet is melted to make a cube

Let the edge be “a”

Hence, a³ = 216 cm³

a = 6 cm

Solution: The correct answer is option (a) 12 cm

Explanation:

Given that, the sum of the volume of the three metal cubes = 6³ + 8³ +10³

V = 216+ 512+ 1000

V = 1728 cm³

Let the side of the new cube be “a”

Therefore, the volume of the new cube = sum of the volume of the three cubes

a³ = 1728

Hence, a = 12 cm

Solution: The correct answer is option (c) 82,125 cm³

Explanation:

The thickness of the wooden box is 2.5 cm

Then the outer measure of the wooden box be 115+5, 75+5, 35+5

Thus, the outer volume be = (120)(80)(40)

Outer volume = 384000 cm³

Given that, the inner volume = (115)(80)(40)

Inner volume = 301875 cm³

Hence, the volume of a wood = Outer volume – Inner volume

V = 384000 – 301875 cm³

V= 82125 cm³

Solution: The correct answer is option (a) 1:6

Explanation:

Assume that r and R be the radii of the two cylinders and h and H be the height of the two cylinders

It is given that r/R = ½ and h/H = 2/3

We know that the volume of a cylinder = πr² h

Now, v/V = πr² h / πR² H

v/ V = (r/R)² (h/H)

v/V = (1/2)² (2/3)

v/V = (1/4) (2/3) = 1/6

Therefore, the ratio of their volume is 1/6

Solution: The correct answer is option (c) 1:16

Explanation:

Let a and b be two cubes

It is given that a³/b³ = 1/64

Then a/b = 1/4

Thus, the ratio of the areas is:

(a/b)² = (1/4)² = 1/16

Solution: The correct answer is option (a) 192

Explanation:

It is given that the solid has a rectangular face, hence,

lb=16 …(1)

bh = 32 ….(2)

lh = 72 …(3)

Multiply the equations (1), (2), (3), we will get

(l)²(b) ² (h) ² = (16)(32)(72) = 36864

lbh = 192

Therefore, the volume of a solid is 192 cubic centimetre.

Solution: The correct answer is option (c) C, A, B

Explanation:

(i) If the cylinder has radius r and height h, then the volume will be πr²h

(ii) If the cylinder has radius 2r and height (1/2)h, then the volume will be 2πr²h

(ii) The volume of the cuboidal container with dimensions is r² h

Then, the arrangement of the containers in the increasing order of their volumes is C, A, B

Solution: The correct answer is option (c) 2 πrh + πR²

Explanation:

The total surface area of a hat = CSA + TSA + Base Surface Area

= 2πrh + πr² + π (R²-r²)

= 2πrh + πR²

In questions 29 to 52, fill in the blanks to make the statements true.

Solution: 24

Explanation: Given that, the cube side is 4 cm, then the volume of the cube is 4³ = 64 cm³

When it is sliced into 1 cubic cm, we will get 64 small cubes

In each side of the larger cube, the smaller cubes on the edges should have more than one face painted. Therefore, the cube, which is located at the corner of the larger cube, has three faces painted.

Hence, on each edge, two small cubes are left, in which two faces are painted.

It is known that the total number of edges in the cube = 12.

Thus, the number of small cubes with two faces painted = 12 × 2 = 24 small cubes.

Solution: No change

Explanation:

Volume of cube = 5³ = 125

Now, when the cube is cut into 1 cubic cm, we will get 125 small cubes

Therefore, the volume of the big cube = volume of 125 cm with 1 cubic cm.

It means that, there is no change in the volume.