Surface Areas & Volumes | Exercise 13.5 | Q8

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.

Video Explanation

Explanatory Answer | Exercise 13.5 Q8

Step 1: Compute the side of the new cube

Side of the larger cube, a = 12 cm
Volume of the larger cube = a³
= 12³
= 1728 cm³

Volume of 8 small new cubes = Volume of the large cube
Let s be the side of the small new cubes.
Volume of each small cube = s³
Therefore, 8 × s³ = 1728
Or s³ = \\frac{1728}{8})
s³ = 216
s = 6 cm

Step 2: Compute the surface area of the cubes

Side of each small cube, s = 6 cm; side of large cube = 12 cm.
Surface area of large cube = 6 a² = 6 × 12²
Surface area of small cube = 6 s² = 6 × 6²
Ratio of their surface areas = \\frac{6×122}{6×6^2})
= \\frac{12×12}{6×6})
= \\frac{4}{1})
Ratio of their surface areas = 4 : 1

Exercise 13.1 | Surface Area of Cubes & Cuboids

1. Class 9 Exercise 13.1 Question 3 | Height of hall ▶
2. Class 9 Exercise 13.1 Question 6 | TSA of Herbarium ▶
3. Class 9 Exercise 13.1 Question 7 | Shanti Sweets ▶

Exercise 13.2 | Surface Area of Cylinders

1. Class 9 Exercise 13.2 Question 3 | CSA TSA of Metal Pipe ▶
2. Class 9 Exercise 13.2 Question 4 | Roller & Playground ▶
3. Class 9 Exercise 13.2 Question 9 | Cylindrical Petrol Tank ▶
4. Class 9 Exercise 13.2 Question 10 | CSA of Decorative Lampshade ▶

Exercise 13.3 | Surface Area of Cones

1. Class 9 Exercise 13.3 Question 5 | Length of Tarpaulin 3 m wide ▶
2. Class 9 Exercise 13.3 Question 8 | Cost of painting conical barricades ▶

Exercise 13.4 | Surface Area of Spheres & Hemispheres

1. Class 9 Exercise 13.4 Question 8 | Outer CSA of hemispherical bowl ▶
2. Class 9 Exercise 13.4 Question 9 | Surface area of sphere & Cylinder ▶