Advertisements
Advertisements
Question
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 (a) of cube = 12 cm
Volume of cube = (a)3 = (12 cm)3 = 1728 cm3
Let the side of the smaller cube be a1.
`"Volume of 1 smaller cube "=(1728/8)cm^3=216cm^3`
(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 cube"/"Surface area of smaller cube"`
`=(6a^2)/(6a_1^2) = 12^2/6^2 = 4/1`
Therefore, the ratio between the surface areas of these cubes is 4:1.
APPEARS IN
RELATED QUESTIONS
A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What will be the volume of a packet containing 12 such boxes?
If V is the volume of a cuboid of dimensions a, b, c and S is its surface area, then prove that
`1/V=2/S(1/a+1/b+1)`
A field is in the form of a rectangle of length 18 m and width 15 m. A pit, 7.5 m long, 6 m broad and 0.8 m deep, is dug in a corner of the field and the earth taken out is spread over the remaining area of the field. Find out the extent to which the level of the field has been raised.
A child playing with building blocks, which are of the shape of the cubes, has built a structure as shown in Fig. 18.12 If the edge of each cube is 3 cm, find the volume of the structure built by the child.
Find the volume of a cuboid whose dimensions are length = 60 m, breadth = 25 m, height = 1.5 m
The dimensions of a match box are 6 cm × 3.5 cm × 2.5 cm. Find the volume of a packet containing 12 such match boxes
The volume of a container is 1440 m3. The length and breadth of the container are 15 m and 8 m respectively. Find its height
The volume of a cuboid is 660 cm3 and the area of the base is 33 cm2. Its height is
A truck carrying 7.8 m3 concrete arrives at a job site. A platform of width 5 m and height 2 m is being contructed at the site. Find the length of the platform, constructed from the amount of concrete on the truck?
A swimming pool is 200 m by 50 m and has an average depth of 2 m. By the end of a summer day, the water level drops by 2 cm. How many cubic metres of water is lost on the day?
