NCERT Solutions Class 9 Maths Chapter 13 — Surface Areas & Volumes

Solution:

Step 1: The area of the four walls is the Lateral Surface Area (LSA) of the cuboid, which is 2h(l + b).

Step 2: The ceiling is one of the faces with dimensions length (l) and breadth (b). Its area is lb.

Step 3: Since the floor is not painted, the total area to be painted is the sum of the LSA and the area of the ceiling. [Total Area = LSA + Area of ceiling = 2h(l + b) + lb]

Solution:

Step 1: Let the original side length of the cube be 'a'.

Step 2: The original Lateral Surface Area (LSA) of the cube is 4a².

Step 3: If the side length is doubled, the new side length becomes '2a'. The new LSA will be 4 × (2a)² = 4 × (4a²) = 16a².

Step 4: Comparing the new LSA (16a²) to the original LSA (4a²), the increase is 16a² / 4a² = 4 times.

Solution:

Step 1: The problem states that the label covers only the 'curved part' of the can, from top to bottom.

Step 2: The curved part of a cylinder is specifically known as its Curved Surface Area (CSA).

Step 3: The Total Surface Area would include the top and bottom circular bases, which are not covered by the label. Volume is the space occupied, not the surface.

Solution:

Step 1: The Total Surface Area (TSA) of a cuboid is 2(lb + bh + hl).

Step 2: For l=5, b=3, h=2, TSA = 2(5×3 + 3×2 + 2×5) = 2(15 + 6 + 10) = 2(31) = 62 cm².

Step 3: The correct calculation yields 62 cm². The statement implies a conceptual mistake in derivation, not the final number. The TSA formula is derived by finding the area of the three unique faces (lb, bh, hl) and then multiplying their sum by 2, because each face has an identical opposite face.

Step 4: Therefore, if Ravi conceptually understood it as 'sum of unique faces multiplied by 2', it's the correct conceptual approach to derive the formula. The question's premise is tricky, suggesting Ravi *might* have made a conceptual mistake, even if the answer is correct. The correct option identifies the *correct* conceptual understanding as a potential 'mistake' if the teacher expected a different explanation, but it highlights that the approach leading to the correct answer *is* the standard derivation. This means options A, B, C describe actual errors that would lead to a wrong answer.

Solution:

Step 1: A cube has 6 identical square faces, each with an area of a².

Step 2: The Lateral Surface Area (LSA) includes the area of the four side faces. So, LSA = 4 × a² = 4a².

Step 3: The Total Surface Area (TSA) includes the area of all six faces. So, TSA = 6 × a² = 6a².

Step 4: Therefore, the statement 'The LSA is 4a²' is true.