RD Sharma Solutions - Class 9 Maths - Chapter 18 - Ex 18.1

Sep 18, 2026

Uploaded by Grenda

RD Sharma Class 9 Maths Chapter 18 Exercise 18.1 contains a set of surface-area based word problems and computations. It covers lateral and total surface areas of cuboids, lateral and total surface areas of cubes, ratios between total and lateral surface areas, and sheet requirements using area of cuboid surfaces. Additional problems address whitewashing and painting cost using room or box surface areas, tile coverage on a cubical tank excluding the base, percent increase in surface area under edge scaling, and determining dimensions from cost differences at different rates.

LanguageEnglish

CategoryExam

FormatPDF

Pages11

Reading Time28 min

AccessFree to download

Lateral and total surface area of a cuboid

Lateral and total surface area of a cube

Ratio of TSA to LSA for a cube

Sheet/tile requirement from cuboid surface area

Whitewashing cost for walls and ceiling

Surface-area ratio after combining cubes into a cuboid

Total surface area after cutting a cube into smaller cubes

Height of a hall from equality of areas

Tile cost for a cubical tank excluding base

Q10

Percentage increase in surface area when edge increases

Q11

Dimensions of a box from cost difference

Q12

Cost of iron sheet for a closed tank

Q13

Tarpaulin area for a shelter (top + four sides)

Q14

Painting cost for inner surface of an open box

# RD SHARMASolutionsClass 9 MathsChapter 18Ex 18.1 Q1)Find the lateral surface area and total surface area of a cuboid of length 80 cm,breadth 40 cm and height 20cm. Solution:Given that: Cuboid length (I)=80cmBreadth (b)=40cmHeight(h)=20cmWe know that, Total Surface Area=2[lb+bh+hl]=2[(80)(40)+(40)(20)+(20)(80)]=2[3200+800+1600]=2[5600]=11200 cm² Lateral Surface Area=2[l+b]h=2[80+40]20=40[120]=4800 cm² Q2)Find the lateral surface area and total surface area of a cube of edge 10 cm.Solution: Cube of edge(a)=10 cmWe know that, Cube Lateral Surface Area =4 a²=4(10*10)=400 cm² Total Surface Area=6 a²=6*10²=600 cm² Q3)Find the ratio of the total surface area and lateral surface area of a cube.Solution: Total Surface Area of the Cube(TSA)=6a²Where,a=edge of the cube And,Lateral surface area of the Cube (LSA)=4 a²Where,a =edge of the cube Hence,Ratio of TSA and Q4)Mary wants to decorate her Christmas tree.She wants to place the tree on a wooden block covered withcolored paper with a picture of Santa Claus on it.She must know the exact quantity of paper to buy for thispurpose.If the box has length,breadth,and height as 80 cm,40 cm and 20 cm respectively.How many squaresheets of paper of side 40 cm would she require? Solution: Given that: Mary wants to paste a paper on the outer surface of the wooden block.The quantity of the paper required would beequal to the surface area of the box which is of the shape of a cuboid. The dimensions of the wooden block are: Length (I)=80cm Breadth (b)=40cm Height(h)=20cm Surface Area of the wooden box=2[lb+bh+hl] =2[(80*40)+(40*20)+(20*80)]=2[5600]=11200 cm² The Area of each sheet of the paper=40×40 cm² =1600 cm² =7 So,she would require 7 sheets. Q5)The length,breadth,and height of a room are 5m,4 m and 3 m respectively.Find the cost of whitewashing thewalls of the room and the ceiling at the rate of Rs 7.50 m². Solution: Total Area to be washed =lb+2(I+b)hWhere,length (1)=5mbreadth (b)=4mheight(h)=3m Therefore,the total area to be white washed is =(5*4)+2*(5+4)*3 =74m² Now,The cost of white washing 1m²is Rs.7.50 Therefore,the cost of white washing 74 m²=(74*7.50) =Rs.555/- Q6)Three equal cubes are placed adjacently in a row.Find the ratio of a total surface area of the new cuboid tothat of the sum of the surface areas of the three cubes. Solution: Length of the new cuboid=3a Breadth of the cuboid =a Height of the new cuboid=a The Total surface area of the new cuboid(TSA)=2(1b+bh+hl) (TSA)₁=2(3a*a+a*a+a*3a)(TSA)₁=14a² The Total Surface area of three cubes (TSA)₂=3*6a²(TSA)₂=18a² T herefore, T herefore,Ratio is 7:9 Q7)A 4cm cube is cut into 1 cm cubes.Calculate the total surface area of all the small cubes.Solution: Edge of the cube(a)=4cm Volume of the cube=a³ =4³ =64cm³ Edge of the cube=1cm³ Therefore, Therefore,Total Surface area of all the cubes =64*6*1=384cm² Q8)The length of a hall is 18m and the width 12m.The sum of the areas of the floor and the flat roof is equal tothe sum of the areas of the four walls.Find the height of the hall. Solution: Length of the hall=18mWidth of the hall =12mNow given, Area of the floor and the flat roof =sum of the areas of four walls→2*1b=2*1h+2*bh→1b=1h+bh Q9)Hameed has built a cubical water tank with lid for his house,with each other edge 1.5m long.He gets theouter surface of the tank excluding the base,covered with square tiles of side 25cm.Find how much he wouldspend for the tiles if the cost of tiles is Rs 360 per dozen. Solution: Given that Hameed is getting 5 outer faces of the tank covered with tiles,he would need to know the surface area of the tank,to decide on the quantity of tiles required. Edge of the cubical tank(a)=1.5m =150cm So,surface area of the tank=5*150*150cm² =180 Cost of 1 dozen tiles,i.e.,cost of 12 tiles =Rs 360 So,the cost of 180 tiles =180*30=Rs.5400 Q10)Each edge of a cube is increased by 50%.Find the pe

FAQs

How do you find the total and lateral surface areas of a cuboid?

Total surface area is calculated as 2(lb + bh + hl), and lateral surface area is calculated as 2(l + b)h, using the cuboid’s length, breadth, and height.

What is the lateral surface area and total surface area of a cube of edge a?

Lateral surface area is 4a² and total surface area is 6a².

If the edge of a cube is increased by 50%, by what percentage does its surface area increase?

The edge becomes 1.5a, so surface area scales by (1.5)² = 2.25. Hence the surface area increases by 125%.

Sep 18, 2026

Uploaded by Grenda