Lateral surface Area of cuboid

Q.

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 $m^2.$

Q.

An open box is made of wood 3 cm thick. Its external length, breadth and height are 1.48 m, 1.16 m and 8.3 dm. Find the cost of painting the inner surface of Rs 50 per sq. metre.

Q.

The length, breadth and height of a cuboid are 15 m, 6 m, and 5 dm respectively. The lateral surface area of the cuboid is

$\left(a\right)45c{m}^2\left(b\right)21c{m}^2\left(c\right)201c{m}^2\left(d\right)90c{m}^2$

Q.

The length and breadth of a hall are in the ratio $4:3$ and its height is $5.5m$ . The cost of decorating its walls (including doors and windows) at $Rs.6.60$ per square metre is $Rs.5082$. Find the length and breadth of the room.

Q.

The length of a room is 1.5 times of its breadth. The cost of carpeting the at Rs. 5 per sq. m is Rs. 270 and the cost of papering the four walls at Rs. 10 per $m^2$ is Rs. 1720. If a door and 2 windows occupy 8 sq. m, find the height of the room.

1. 9 m

2. 6 m

3. 4 m

4. 8 m

Q.

The surface area of a cuboid is 1372 $c{m}^2$. If its dimensions are in the ratio 4: 2:1, then its length(in cm) is:

1. 7

2. 14

3. 21

4. 28

Q.

The cost of preparing the walls of a room 12 m long at the rate of Rs 1.35 per square metre is Rs 340.20 and the cost of matting the floor at 85 paise per square metre is Rs 91.80. Find the height of the room.

Q.

The actual length of a painting was $2m$. What is the length of the photograph if the scale used is $1mm:20cm$.

Q.

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.

Q.

How many cubes of side 2 cm can be fit into cuboid box having length, breadth and height of 8cm, 12 cm and 10 cm respectively? [3 MARKS]

Q. If lateral surface area of cuboid is 24 $c{m}^2$ and area of base is 4 $c{m}^2$, then find total surface area of cuboid.

1. 42 $c{m}^2$
2. 52 $c{m}^2$
3. 32 $c{m}^2$
4. 92 $c{m}^2$

Q. Find the lateral surface area and total surface area of a cuboid of length 80 cm, breadth 40 cm and height 20 cm.

Q. Question 18

In a blueprint of a room, an architect has shown the height of the room as 33 cm. If the actual height of the room is 330 cm, then the scale used by her is
(a) 1 : 11
(b) 1 : 10
(c) 1 : 100
(d) 1 : 3

Q.

If a cube fits exactly in a cylinder with a height of h, then the volume of the cube is __________ and the surface area of the cube is __________.

Q.

The dimensions of a room are 12.5 m by 9 m by 7 m. There are 2 doors and 4 windows in the room; each door measures 2.5 m by 1.2 m and each window 1.5 m by 1 m. Find the cost of painting the walls at Rs 3.50 per square metre.

Q. The volume of a rectangular block of stone is 10368 $m^3$. If its length, breadth and height are in the ratio 3 : 2 : 1, then its length, breadth and height are

1. 12 m, 8 m, 4 m
2. 36 m, 24 m, 12m
3. 9 m, 6 m, 3 m
4. 39 m, 26 m, 13 m

Q.

Rukshar painted the outside of the cabinet to measure $1m$ $\times 2m$ $\times 1.5m$ . How much surface area did she cover if she painted all except the bottom of the cabinet?

Q.

A box has length, breadth and height of 10 cm, 20 cm and 5 cm respectively. The lateral surface area of the box is ______.

1. 100 $c{m}^2$​
2. 200 $c{m}^2$​
3. 300 $c{m}^2$​
4. 400 $c{m}^2$​

Q. The base of a triangular field is three times its altitude. If the cost of sowing the field at Rs. $58$ per hectare is Rs. $783$, find its base and height.

Q. The floor of a rectangular hall has a perimeter 250m. If the cost of panting the four walls at the rate of Rs.10 per $m^2$ is Rs.15000, find the height of the hall.

Q. The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is 5$\sqrt{5}$cm. Its surface area is

(a) 361 cm²

(b) 125 cm²

(c) 236 cm²

(d) 486 cm²

Q.

A tank with length, breadth and height of $5,6$ and $3$ units respectively is open from the top. The cost of anti-microbial coating inside the tank at ₹ 10 per sq. unit is ______.

1. ₹ 1060

2. ₹ 660

3. ₹ 1260

4. ₹ 960

Q. A cuboid has total surface area of 372 cm² and its lateral surface area is 180 cm², find the area of its base.

Q. A cuboid has total surface area of 40 m² and lateral surface area of 26 m². Find the area of it base.

Q.

A box has length, breadth and height of 10 cm, 20 cm and 5 cm respectively. The lateral surface area of the box is ______.

1. 200 $c{m}^2$​
2. 100 $c{m}^2$​
3. 300 $c{m}^2$​
4. 400 $c{m}^2$​

Q. If V is the volume of a cuboid of dimensions a × b × c and A is its surface area, then $\frac{A}{V}$ is

1. $a^2{b}^2{c}^2$
2. $2(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})$
3. $\frac{1}{abc}$
4. $\frac{1}{2}(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca})$

Q. For the given statements, choose the correct option:
Assertion (A): Volume of a hemisphere is $\frac{4}{3}\pi r^3.$
Reason (R): Volume of cone is $\frac{1}{3}\pi r^2.$

(A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).​

(B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).​

(C) Assertion (A) is true but reason (R) is false.​

(D) Assertion (A) is false but reason (R) is true.​

[1 Mark]

Q.

If $\mathit{V}$ is the volume of a cuboid of dimensions $\mathit{a}$, $\mathit{b}$, $\mathit{c}$ and $\mathit{S}$ is its surface area, then prove that: $\frac{\mathbf{1}}{\mathbf{V}}\mathbf{=}\frac{\mathbf{2}}{\mathbf{S}}\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)$.

Q.

A box has length, breadth and height of 10 cm, 20 cm and 5 cm respectively. The lateral surface area of the box is

1. 100 cm²

2. 200 cm²

3. 300 cm²

4. 400 cm²

Q. Find the lateral surface area and the total surface area of a cuboid of dimensions 40 cm × 30 cm × 20 cm.