Real Life Application

Q. A tent is in the form of a cylinder surmounted by a cone. The slant height of the cone is 10 m, and height of the cylinder is 8 m. If the diameter of the cylinder is 12 m, then find the total surface area of the tent.

1. $490.2m^2$
2. $390.2m^2$
3. $290.2m^2$
4. $690.2m^2$

Q.

Two cubes, each of edge length 12 cm are joined end to end. Find the surface area of the resulting cuboid.

1. $1450c{m}^2$

2. $1440c{m}^2$

3. $1420c{m}^2$

4. $1410c{m}^2$

Q. A tank with length, breadth and height of 8, 6 and 4 units respectively is open at the top. Find the cost of painting inside the tank at the rate of ₹10 per sq.units.

1. $₹1500$
2. $₹1600$
3. $₹1400$
4. $₹1450$

Q. Match the following solid objects with the expressions of their volume.

1. ${\mathrm{\pi r}}^{2}h-\frac{1}{3}{\mathrm{\pi r}}^{2}h$
2. ${\mathrm{\pi r}}^{2}h+\frac{2}{3}{\mathrm{\pi r}}^3$
3. $2{{\mathrm{\pi r}}_1}^2{h}_1+{{\mathrm{\pi r}}_2}^2{h}_2$

Q. When the entire water from a river is used to irrigate a field for a given time interval, what should be equal for both the river and the field.

1. Length and breath
2. Breadth and height
3. Surface area
4. Volume

Q.

The volumes of the two cubes are in the ratio 64:27. Find the ratio of their surface areas.

1. $9:18$

2. $16:25$

3. $16:9$

4. $4:3$

Q.

A road roller was used for levelling a road of width 2 m. It was observed that, the road roller required 25 complete revolutions to level the entire road. If the radius and the length of the roller is 7 m and 2 m respectively, then length of the road is ____. [Take $\pi$ = 3.14].

1. 1200 m

2. 1234 m

3. 2100 m

4. 1100 m

Q. If an iron ball is melted and recasted into 3 small spherical balls of radius 3 cm, 4 cm and 5 cm, then the radius of the larger iron ball is .

1. 6 cm
2. 12 cm
3. 18 cm
4. 24 cm

Q. A solid object made up of wood is in the shape of a cylinder with 4 cuboidal depressions. The radius and height of the cylinder is 7 cm and 10 cm, respectively. The dimensions of the cuboid are 2 cm $\times$ 3 cm $\times$ 4 cm. Find the volume of wood in the solid object.

1. $3918c{m}^3$
2. $7024c{m}^3$
3. $789c{m}^3$
4. $1444c{m}^3$

Q.

Consider the following three statements.
Statement-1: The lateral surface area of a cuboid shaped room $=$ the perimeter of the rectangular floor $\times$ height of the room.
Statement-2 : Total surface area of a cylinder $=$ circumference of the circular base $\times$ (diameter of the base $+$ height of the cylinder).
Statement-3 : Curved surface area of a cone $=\frac{1}{2}\times$ slanting height of the cone $x$ circumference of the base of the cone.

Which of the following is correct?

1. Statements 1 and 3 are true and statement 2 is false.

2. Statements 1 and 2 are false and statement 3 is true.

3. Statement 1 and 3 are false and statement 2 is true.

4. All statements are true.

Q. When we mould and recast a solid from one shape to another, its remains the same.

1. surface area
2. volume
3. height

Q.

The cost of painting the inner curved surface area of a cylindrical container of depth 20 m is ₹ 8800. If the painter charges ₹ 40 per metre square to paint the cylindrical container, then find its radius.
[ $\text{Take}\pi =\frac{22}{7}$ ]

1. 1.75 m

2. 3.5 m

3. 7 m

4. 6 m