Question

18.14
MATHEMATICS-IX
EXERCISE 18.1
1. Find the lateral surface area and total surface area of a cuboid of length 80 cm, breadth
40 cm and height 20 cm.
2. Find the lateral surface area and total surface area of a cube of edge 10 cm.
3. Find the ratio of the total surface area and lateral surface area of a cube.
4. Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden
block covered with coloured paper with 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?
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
6. Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of
the new cuboid to that of the sum of the surface areas of the three cubes.
[NCERT)​

Answer 1

Answer:

1. TSA = 11,200 $m^{2}$ LSA = 4800 $cm^{2}$

2. TSA = 600 $cm^{2}$ LSA = 400 $cm^{2}$

3. 3:2

4. 7 sheets

5. Rs 555/-

6. 7:9

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Answer 2

Answer:

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.