1. A stage (platform) is made with 5 Math-Magic books. The volume of this stage is the same as _____ cm cubes.

2. Guess the volume of these things in cm cubes.
• A matchbox is about cm cubes.
• A geometry box is about _ cm cubes.
• An eraser is about ______ cm cubes.
How will you check your guess? Discuss.

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Solution

1) Volume of 1 Math-Magic book = 540 cm cubes.
5 Math-Magic books are used to make the stage.
So, volume of the stage = Volume of 5 such Math-Magic books
= 5 $\times$ 540 cm cubes
= 2700 cm cubes

2)• A matchbox is about 13.5 cm cubes.
• A geometry box is about 157.5 cm cubes.
• An eraser is about 1.5 cm cubes.

We will multiply the length, breadth and height of the object to cross-check our guess.

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Similar questions

Q. Tanu is making a stage with matchboxes.
She first puts 14 matchboxes like this in the first layer.
She makes 4 such layers and her stage looks like this.
• She used ________ matchboxes to make this stage.
• The volume of one matchbox is the same as 10 cm cubes.
Then the volume of this stage is same as ________ cm cubes.
• If all these cubes are arranged in a line, how long will that line be? _________ cm.
• Which has more volume — your Math-Magic book or Tanu's platform?
With your friends, collect many empty matchboxes of the same size. Measure the sides and write here.

• Use 56 matchboxes to make platforms of different heights. Fill this table.

	How high is it?	How long is it?	How wide is it?
Platform 1
Platform 2
Platform 3

The volume of each platform is equal to __________ matchboxes.

Q. What is the volume of the geometry box in cm cubes, if its diemsions are as follows?
Length = 16 cm, breadth = 6 cm and
height = 1 cm

Q. A cube whose volume is 1/8 cubic centimeter is placed on top of a cube whose volume is 1 cm³. The two cubes are then placed on top of a third cube whose volume is 8 cm³. The height of the stacked cubes is

(a) 3.5 cm

(b) 3 cm

(c) 7 cm

(d) none of these

Q. Question:

Question 8
A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.

Mathematics Surface Areas and Volumes Volume of Solids
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Solution:

Side(a) of the cube = 12 cm

Volume of the cube =(a)3=(12 cm)3=1728 cm3

Let the side of the smaller cube be a1.

Volume of 1 smaller cube =(17288)cm3=216 cm3(a1)3=216 cm3⇒a1=6 cm

Therefore, the side of the smaller cubes will be 6 cm.

Ratio between surface areas of cubes =Surface area of bigger cubeSurface area of Smaller cube=6×1226×62=(12)2(6)2=41

Therefore, the ratio between the surface areas of these cubes is 4:1.

my doubt is how this a1 got 6cm

Q. The volume of the cube is

27 c m^{3}

. If this cube is cut into 9 smaller cubes then, what's the volume of each smaller cube?

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