Lateral surface area of a cube

Q.

Find the lateral surface area and total surface area of a cube of edge 10 cm.

Q.

Three cubes of metal with edges 3 cm, 4 cm, and 5 cm respectively are melted to form a single cube. The lateral surface area of the new cube formed is

$\left(a\right)72c{m}^2\left(b\right)144c{m}^2\left(c\right)128c{m}^2\left(d\right)256c{m}^2$

Q.

Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much be would spend for the tiles, if the cost of tiles is Rs. 360 per dozen.

Q.

If the perimeter of each face of a cube is 32 cm, find its lateral surface area. Note that four faces which meet the base of a cube are called its lateral faces.

Q. Find the lateral surface area of a cubical lamp of edge 10 cm.

1. 40 $c{m}^2$
2. 200 $c{m}^2$
3. 400 $c{m}^2$
4. 440 $c{m}^2$

Q. Question 5
A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.
(i) Which box has the greater lateral surface area and by how much?
(ii) Which box has the smaller total surface area and by how much?

Q. A mixture contains milk and water in the ratio $5:1.$ On adding $5$ litres of water, the ratio of milk to water becomes $5:2.$ The quantity of milk in the original mixture is

1. $16$ litres
2. $22.75$ litres
3. $32.5$ litres
4. $25$ litres

Q. What is the length of the side of the cube if its lateral surface area is $4{\text{cm}}^2$?

1. 3 cm
2. 1 cm
3. 4 cm
4. 2 cm

Q.

The surface area of a cuboid formed by joining two cubes of side $a$ face to face is __________.

Q. Three identical cubes of side 5cm are joined end to end. Find the total surface area and lateral surface area f the resulting cuboid so formed.

1. TSA= 300 cm${}^2$ CSA= 100 cm${}^2$
2. TSA = 360 cm${}^2$ CSA = 190 cm${}^2$
3. TSA = 350 cm${}^2$ CSA = 200 cm${}^2$
4. TSA = 366 cm${}^2$ CSA = 133 cm${}^2$

Q.

Find the volume, the lateral surface area, the total surface area and the diagonal of a cube, each of whose edges measures 9m. $(Take\sqrt{3}=\mathrm{1.73.})$

Q. What is the percentage increase in the lateral surface area of a cube, if each of its side is increased by 50% ?

1. 125%
2. 25%
3. 100%
4. 135%

Q.

Find the volume, the lateral surface area, the total surface area and the diagonal of a cube, each of whose edges measures 9m. $(Take\sqrt{3}=\mathrm{1.73.})$

Q.

The lateral surface area of a cube is $100m^2$. The volume of the cube is

1. $25m^3$

2. $125m^3$

3. $1000m^3$

4. $100m^3$

Q.

Three metallic solid cubes whose edges are 3 cm, 4 cm and 5 cm are melted and formed into a single cube. Find the edge of the cube so formed.

1. 9cm

2. 7cm

3. 6cm

4. 8cm

Q. LSA of cube having side 3 cm is

1. $27{\text{cm}}^2$
2. $36{\text{cm}}^2$
3. $9{\text{cm}}^2$
4. $18{\text{cm}}^2$

Q. A solid cube of side $12$ cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.

Q.

If the length of diagnal of a cube is $8\sqrt{3}cm$ then its surface area is

$\left(a\right)192c{m}^2\left(b\right)384c{m}^2\left(c\right)512c{m}^2\left(d\right)768c{m}^2$

Q. If LSA of a cube is 100 cm${}^2$, then its side is:

1. 5 cm
2. 10 cm
3. 25 cm
4. 6 cm

Q.

Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25cm. Find how much he would spend for the tiles, if the cost of the tiles is ₹360 per dozen.

Q.

Find the volume, the lateral surface area, the total surface area and the diagonal of a cube, each of whose edges measures 9m. $(Take\sqrt{3}=\mathrm{1.73.})$

Q. Question 6
A cube of side 4 cm contains a sphere touching its sides. Find the volume of the gap in between.

Q. The total surface area of a cube is $384m^2$. Its volume will be:

1. $616m^3$
2. $512m^3$
3. $343m^3$
4. $660m^3$

Q.

Determine the ratio of the lateral surface area to total surface area of a cube.

1. $\frac{3}{2}$

2. $\frac{2}{3}$

3. 1

4. $\frac{4}{9}$

Q. If the lateral surface area of a cube is $1600c{m}^2$, then its edge is

1. $15cm$
2. $18cm$
3. $20cm$
4. $25cm$

Q.

Determine the ratio of the lateral surface area to total surface area of a cube.

1. $\frac{3}{2}$

2. $\frac{2}{3}$

3. 1

4. $\frac{4}{9}$

Q. Three containers have their volumes in the ratio $3:4:5.$ They are full of mixtures of milk and water. The mixtures contain milk and water in the ratio of $(4:1),(3:1)$ and $(5:2)$ respectively. The ratio of milk and water in the fourth container which contains mixture of all the above three mixtures is

1. $4:1$
2. 
   
   $157:53$
3. $151:48$
4. $5:2$

Q. Find the surface area of a conical hat, if its slant height is three times the radius and the base diameter of a hat is $4$ inches. (Use $\pi =3$).

1. $48{in}^2$
2. $36i{n}^2$
3. $48in$
4. $46{in}^2$

Q. LSA of cube having side 3 cm is

1. $27{\text{cm}}^2$
2. $36{\text{cm}}^2$
3. $9{\text{cm}}^2$
4. $18{\text{cm}}^2$

Q. The lateral surface area of a cube of side a is ______ .

1. $4a^2$
2. $6a^2$
3. $12a^2$
4. $2a^2$