Question

Q.10. Susan likes to build blocks from small cubes like the one shown in the following

Diagram :



Small cube (A) (B) (C)

Susan has lots of small cubes like this one. She uses glue to join cubes together to make

other blocks. First, Susan glues eight of the cubes together to make the block shown in

Diagram A. Then Susan makes the solid blocks shown in Diagram B.

(a)How many small cubes will Susan need to make the block shown in Diagram B?

(b) Susan realises that she could have glued small cubes together to look like

Diagram C, but the block could have been hollow on the inside.

What is the minimum number of cubes she needs to make a block that looks like

the one shown in Diagram C, but is hollow?

(c)Now Susan wants to make a block that looks like a solid block that is 5 small cubes long, 4

small cubes wide and 3 small cubes high. How many small cubes will be required to make the

block ?​

Answer 1

Given : Susan likes to build blocks from small cubes

Shown in fig

To Find : (a)How many small cubes will Susan need to make the block shown in Diagram B?

b)  minimum number of cubes she needs to make a block that looks like

the one shown in Diagram C, but is hollow?

c)   How many small cubes for a block that looks like a solid block that is 5 small cubes long, 4  small cubes wide and 3 small cubes high.

Solution:

small cubes Susan need to make the block shown in Diagram B

=  3 * 2 * 2

= 12   small cubes

minimum number of cubes she needs to make a block that looks like

the one shown in Diagram C

= 3 * 3 * 3

= 27 small cubes

if its hollow  then cubes which can be removed = (3 -2)(3 - 2)(3 -2 ) = 1

Hence small cubes required = 27 - 1 = 26  for Hollow C

 a solid block that is 5 small cubes long, 4  small cubes wide and 3 small cubes high.

small cubes required = 5 *  4  * 3  = 60  

if hollow then cubes can be removed = (5 - 2)(4 - 2) (3 - 2) = 6

Hollow block will require 60 - 6 = 54   small cubes

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