RD Sharma Solution Class 9 Maths Chapter 18 - Surface Area and Volume of Cuboid and Cube - Exercise 18.1

Sep 18, 2026

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Exercise 18.1 covers problems on surface areas of cuboids and cubes using standard geometry formulas. It computes lateral surface area and total surface area for given cuboid dimensions, finds lateral and total surface areas for a cube, and derives the ratio between them. Word problems include sheet-covering requirements for a wooden block, cost of whitewashing walls and ceiling, comparisons using combined solids, and surface areas formed by cutting cubes into smaller cubes. It also solves a hall-height equation and a tiled cubical tank cost, concluding with percentage increase in cube surface area.

LanguageEnglish

CategoryExam

FormatPDF

Pages16

Reading Time40 min

AccessFree to download

Exercise 18.1

Lateral and total surface area of a cuboid

Lateral and total surface area of a cube

Ratio of total to lateral surface area for a cube

Surface-area-based paper covering for a wooden block

Whitewashing walls and ceiling cost

Ratio after forming a new cuboid from cubes

Total surface area after cutting a cube into small cubes

Finding hall height from area relationships

Tile cost for a cubical tank excluding base

Percentage increase in surface area when cube edge increases 50%

Exercise 18.1 Page No: 18.14 Question 1: Find the lateral surface area and total surface area of a cuboid of length 80 cm, breadth 40 cm and height 20 cm. Solution: Given, Dimensions of a cuboid: Length (l) = 80 cm Breadth (b) = 40 cm Height (h) = 20 cm We know that, Total Surface Area = 2[lb + bh + hl] By substituting the values, we get = 2[(80)(40)+(40)(20)+(20)(80)] = 2[3200+800+1600] = 2[5600] = 11200 Therefore, Total Surface Area = 11200 cm2 Now, Lateral Surface Area = 2[l + b]h = 2[80+40]20 = 40[120] = 4800 Thus, Lateral Surface Area is 4800 cm2. Question 2: Find the lateral surface area and total surface area of a cube of edge 10 cm. Solution: Side of a Cube = 10 cm (Given) Formula for Cube Lateral Surface Area = 4 side2 Cube Lateral Surface Area = 4(10 x 10)= 400 cm2 Total Surface Area = 6 Side2 = 6(102) = 600 cm2 Question 3: Find the ratio of the total surface area and lateral surface area of a cube. Solution: Total Surface Area of the Cube (TSA) = 6 Side2 Lateral surface area of the Cube (LSA) = 4 Side2 Now, Ratio of TSA and LSA = (6 Side2)/ (4 Side2) = 3/2 or 3:2 . Question 4: Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden block covered with colored paper with a picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box has length, breadth, and height as 80 cm, 40 cm and 20 cm respectively. How many square sheets of paper of side 40 cm would she require? Solution: The dimensions of the wooden block are: Length (l) = 80cm Breadth (b) = 40cm Height (h) = 20cm Surface Area of the wooden box = 2[lb + bh + hl]= 2[(80x40)+(40x20)+(20x80)] = 2[5600] = 11200 Surface Area of the wooden box is 11200 cm2 The Area of each sheet of the paper = 40×40 cm2 = 1600 cm2 Now, The total number of sheets required = (Surface area of the box )/(Area of one sheet of paper) = 11200/1600 = 7 Therefore, Marry would require 7 sheets. Answer!! Question 5: The length, breadth, and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs 7.50 m2. Solution: Formula: Total Area to be washed = lb + 2(l + b)h (1) Where, l = length , b = breadth and h = height. From given: Length = l = 5 m Breadth = b = 4 m Height = h = 3 m Total area to be white washed = (5x4) + 2(5 + 4)3 (using (1)) = 74 Total area to be white washed is 74 m2 Now, cost of white washing 1 m2 is Rs. 7.50 (Given) Therefore, the cost of white washing 74 m2 = (74 x 7 .50)= Rs. 555 Question 6: Three equal cubes are placed adjacently in a row. Find the ratio of a total surface area of the new cuboid to that of the sum of the surface areas of the three cubes. Solution: Let breadth of the cuboid = a Then, length of the new cuboid = 3a and Height of the new cuboid = a Now, Total surface area of the new cuboid (TSA) = 2(lb+bh+hl) = 2(3a x a + a x a + a x 3a) = 14a2 Again, Total Surface area of three cubes = 3 x (6 side2 ) = 3 x 6a2 = 18a2 Therefore, ratio of a total surface area of the new cuboid to that of the sum of the surface areas of the three cubes = 14a2/18a2 = 7/9 or 7:9 Therefore, required ratio is 7:9 . Answer. Question 7: A 4 cm cube is cut into 1 cm cubes. Calculate the total surface area of all the small cubes. Solution: Edge of the cube = 4 cm (Given) Volume of the cube = Side3 = 43 = 64 Volume of the cube is 64cm3 Again, Edge of the cube = 1 cm3 So, Total number of small cubes = 64cm3/1cm3 = 64 And, total surface area of all the cubes = 64 x 6 x 1 = 384 cm2 Question 8: The length of a hall is 18 m and the width 12 m. The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls. Find the height of the hall. Solution: Dimensions of the hall are: Length = 18m Width = 12m From statement: Area of the floor and the

FAQs

How do you find the total surface area of a cuboid with given length, breadth, and height?

Use TSA = 2(lb + bh + hl). Substitute the given dimensions and simplify to get the total area in square centimeters.

What is the lateral surface area of a cube, and how is it related to total surface area?

For a cube of side a, LSA = 4a² and TSA = 6a². The ratio TSA:LSA becomes 6a²:4a² = 3:2.

How do you calculate the number of paper sheets needed to cover a box surface?

Compute the box surface area, then divide by the area of one sheet. For each sheet of side 40 cm, its area is 40×40 = 1600 cm², so sheets = (surface area)/(1600).

Sep 18, 2026

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