Question

EXERCISE 11.4
of tin. What is the
A rectangular box of length 40 cm, breadth 25 cm and height 20 cm is to be made of tin. What
area of the tin sheet required, if the box has a lid also?
2. Find the surface area of a cubical water tank of side 15 m.
3. The total surface area of a cube is 96 sq m. What is length of each side?
4. A swimming pool is of dimensions 20 m, 15 m and 4 m. Find the cost of tiling its floor and the walls
at the rate of 12 per square metre.
5. The total surface area of a box of length 8 cm and breadth 6 cm is 208 sq cm. Find the height of the
11.
12
box.
1
6. The total surface area of a cuboid is 40 m² and its lateral surface area is 26 m². Find the area of the
floor.
7. Find the length of the longest rod that can be placed in a room of dimensions 8 m, 10 m and 6 m.​

Answer 1

Q.1 ) A rectangular box of length 40 cm, breadth 25 cm and height 20 cm is to be made of tin. What area of the tin sheet required, if the box has a lid also?

Given:

• Length is 40 cm Breadth is 25 cm and Height is 20 cm

To Find:

• Area of Tin sheet required, if box has a lid also

Solution:

★ Total Surface area of box = 2(lb+bh+hl)

$\small\implies{\sf }$ Area = 2( 40 x 25 + 25 x 20 + 20 x 40 )

$\small\implies{\sf }$ Area = 2( 1000 + 500 + 800 ) = 2 x 2300 = 4600

Hence, Area of tin sheet required will be 4600 cm²

____________________

Q.2) Find the surface area of a cubical water tank of side 15 m.

Given:

• Side of cubical water tank is 15 m

To Find:

• Surface area of water tank

Solution:

★ Total Surface area of Cube = 6(side)²

$\small\implies{\sf }$ Total Surface area = 6 (15)² = 6 x 225 = 1350

Hence, Surface Area of water tank will be 1350 m²

_____________________

Q.3) The total surface area of a cube is 96 sq m. What is length of each side?

Given:

• TSA of cube is 96 m²

To Find:

• Length of each side of cube

Solution:

★ Total Surface Area Of Cube = 6(side)²

$\small\implies{\sf }$ 96 = 6 (side)²

$\small\implies{\sf }$ 96/6 = s²

$\small\implies{\sf }$ √16 = side

$\small\implies{\sf }$ 4 = side

Hence, Length of each side of cube will be 4 cm

________________________

Q.4) A swimming pool is of dimensions 20 m, 15 m and 4 m. Find the cost of tiling its floor and the walls

at the rate of 12 per square metre.

Given:

• Length , Breadth and Height of pool is 20,15 and 4 respectively.

To Find:

• Cost of tiling walls at 12 /m²

Solution:

★ First, We have to find the area of floor and then we have to find Area of walls ★

$\small\implies{\sf }$ Area of floor = Length x Breadth = 20 x 15 = 300m²

$\small\implies{\sf }$ Area of walls = 2 ( bh + hl ) = 2 [(15 x 4 ) + ( 4 x 20 ) ]

$\small\implies{\sf }$ Area of walls = 2 (60+80) = 2 x 140 = 280 m²

→ Add both the areas to get total area

→ (300+280)m² = 580m²

Now, Cost of tiling = 580 x 12 = Rs 6960

_________________________

Q.5) The total surface area of a box of length 8 cm and breadth 6 cm is 208 sq cm. Find the height of the box

Given:

• Length and Breadth of box is 8 cm and 6 cm respectively
• TSA of box is 208 cm²

To Find :

• Height of the box

Solution:

† Let the height be 'h' cm †

★ Total Surface Area Of Cuboid = 2(lb+bh+hl) ★

$\small\implies{\sf }$ TSA = 2(8 x 6 + 6 x h + h x 8)

$\small\implies{\sf }$ TSA = 2(48 + 6h + 8h )

$\small\implies{\sf }$ 208 = 2(48+14h)

$\small\implies{\sf }$ 208 = 96 + 28h

$\small\implies{\sf }$ (208–96)/28 = h

$\small\implies{\sf }$ 112/28 = 4cm = Height

Hence, Height will be 4 cm

_________________________

Q.6) The total surface area of a cuboid is 40 m² and its lateral surface area is 26 m². Find the area of the floor.

Given:

• TSA of Cuboid is 40m² and LSA of Cuboid is 26m²

To Find:

• Area of the floor

Solution:

★ TSA of Cuboid = 2(lb+bh+hl)

$\small\implies{\sf }$ 40 = 2(lb+bh+hl)

$\small\implies{\sf }$ 40/2 = (lb+bh+hl)

$\small\implies{\sf }$ 20 = (lb+bh+hl) ..............(1)

★ LSA of Cuboid = 2h( l + b )

$\small\implies{\sf }$ 26 = 2h(l+b)

$\small\implies{\sf }$ 26/2 = hl + bh

$\small\implies{\sf }$ 13 = hl + bh ..................(2)

Now, substitute equation (2) in (1)

$\small\implies{\sf }$ lb + 13 = 20

$\small\implies{\sf }$ lb = 20–13 = 7 m²

Hence, Area of floor will be 7 m²

_________________________

Q.7) Find the length of the longest rod that can be placed in a room of dimensions 8 m, 10 m and 6 m.

Given:

• Length , Breadth and Height of room are 8 m , 10 m and 6 m respectively

To Find:

• Length of longest rod i.e Diagonal of Cuboid

Solution:

★ Diagonal of Cuboid = √l²+b²+h²

$\small\implies{\sf }$ √8²+10²+6² = √200

$\small\implies{\sf }$ √ 2 x 2 x 2 x 5 x 5

$\small\implies{\sf }$ 2 x 5 x √2 = 10√2

Hence, Length of longest rod that can be placed in room will be 10√2 m