+91-8076753736[email protected]
logo
logo
-->

Probability

Question
CBSEENMA9003485
Wired Faculty App

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. 

Solution

Side of the solid cube (a) = 12 cm
∴ Volume of the solid cube = a3
= (12)3 = 12 x 12 x 12 cm3 = 1728 cm
∵ It is cut into eight cubes of equal volume.
∴ Volume of a new cube
equals 1728 over 8 space cm cubed space equals space 216 space cm cubed

Let the side of the new cube be x cm.
Then, volume of the new cube = x3 cm3. According to the question, x3 = 216
∴    x = (216)1/3
∴    x = (6 x 6 x 6)1/3
∴    x = 6 cm
Hence, the side of the new cube will be 6 cm. Surface area of the original cube = 6a2 = 6(12)2 cm2 Surface area of the new cube
= 6x2 = 6(6)2 cm2
∴ Ratio between their surface areas
equals fraction numerator Surface space area space of space the space original space cube over denominator Surface space area space of space the space new space cube end fraction equals fraction numerator 6 left parenthesis 12 right parenthesis squared over denominator 6 left parenthesis 6 right parenthesis squared end fraction equals 4 over 1 equals 4 space colon space 1

Hence, the ratio between their surface areas is 4: 1.

Some More Questions From Probability Chapter

A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.

(i) Which box has the greater lateral surface area and by how much?

A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high.

(i)    What is the area of the glass?
(ii)    How much of tape is needed for all the 12 edges?

Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions 4 m × 3 m?

A table cover 4 m x 2 m is spread on a table. Find the cost of polishing the top of the table at र40 per square metre of 25 cm table cover is hanging all round the table.

A classroom is 7 m long, 6.5 m wide and 4 m high. It has one door 3 m x 1.4 m and three windows each measuring 2 m x 1 m. The interior wall is to be colour washed. Find the cost of colour washing at the rate of र 3.50 per m2.

Two cubes of side 6 cm each, are joined end to end. Find the surface area of the resulting cuboid.  

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation