Total Surface Area of Prisms

Q.

Two identical prisms with triangles as base are joined to form a rectangular prism as shown below.

What is the total surface area of the rectangular prism?

1. $680c{m}^2$
2. $630c{m}^2$
3. $1260c{m}^2$
4. $760c{m}^2$

Q.

MODELING REAL LIFE A cereal box has a volume of 225 cubic inches. The length of the base is 9 inches and the width of the base is 2.5 inches. What is the height of the box? Justify your answer.

Q.

The base of a prism is an equilateral triangle of perimeter 15 cm and the height is 5 cm. What is the volume of the prism?

1. $\frac{125\sqrt{3}}{4}c{m}^3$
   

2. $\frac{75\sqrt{3}}{4}c{m}^3$
   

3. $\frac{85\sqrt{3}}{4}c{m}^3$
   

4. $\frac{175\sqrt{3}}{4}c{m}^3$

Q.

A triangular wall having sides 3m, 5m and 6m has to be painted. If the cost of painting 1$m^2$ of wall is Rs 5. What is the cost of painting the whole wall?

1. 16√3

2. 10√14

3. 12√14

4. 14√10

Q.

The base of a prism is an equilateral triangle of perimeter 15 cm and its height is 10 cm. What is its total surface area ?

1. $(150+\frac{20\sqrt{3}}{3})c{m}^2$

2. $\left(\frac{300+25\sqrt{3}}{2}\right)c{m}^2$

3. $\left(\frac{300+20\sqrt{3}}{2}\right)c{m}^2$

4. None of these

Q.

The lateral or vertical surface area of a cuboidal box of length, breadth and height 6 cm, 8 cm and 6.5 cm respectively is

1. 186 cm²

2. 182 cm²

3. 146 cm²

4. 172 cm²

Q. Where to use total surface area and where to use lateral surface area if it is not given in question. For example find the surface area of box of dimension 10cm, 15cmand20cm.

Q.

The base of a prism is a right angled triangle having its base and altitude as 12 cm and 16 cm respectively. What is the total surface area of the prism if height of prism is 22 cm?

1. $1296c{m}^2$
   

2. $1148c{m}^2$
   

3. $1248c{m}^2$
   

4. $1295c{m}^2$

Q.

Two identical prisms with base a right angled triangle are joined together to form a rectangular prism, as in the picture below:

What is the surface area of this rectangular prism?

Q.

The base area of a prism is $40c{m}^2$. What would be the height of the prism if its volume = $200c{m}^3$ ?

1. 7 cm

2. 6.3 cm

3. 5 cm

4. 4 cm

Q.

The base of a prism forms a right angled triangle. The triangle has base and height as 4 cm and 6 cm respectively. The height of the prism is 10 cm. The volume of the prism will be :

1. $180c{m}^3$

2. $240c{m}^3$

3. $60c{m}^3$

4. $120c{m}^3$

Q.

The volume of a prism is 100 $m^3$ and its height is $\frac{4}{\sqrt{3}}m$. The base of the prism is an equilateral triangle. What is the length of each side of the triangle forming the base of the prism ?

1. 6 m

2. 10 m

3. 7 m

4. 4 m

Q.

The base of a prism is a rectangle having sides 5 cm and 12 cm respectively. The height of the prism is 18 cm. It is split vertically along the diagonal of the base into two triangular prisms. What is the total surface area of each of the triangular prism?

1. $400c{m}^2$
2. $800c{m}^2$
3. $1200c{m}^2$
4. $600c{m}^2$

Q.

The lateral or vertical surface area of a cuboidal box of length, breadth and height 6 cm, 8 cm and 6.5 cm respectively is

1. 182 cm²

2. 172 cm²

3. 186 cm²

4. 146 cm²

Q.

A solid cylindrical pipe made of wax has a radius of 2 cm and height equal to 14 cm. It is melted and recast into a solid prism of base area $16c{m}^2.$ What will be the height of the prism?

1. 11 cm
2. 12 cm
3. 22 cm
4. 21 cm

Q. Total surface area of cuboid is equal to

1. lateral surface area + 3 x area of base
2. lateral surface area + area of base
3. lateral surface area + 4 x area of base
4. lateral surface area + 2 x area of base

Q. A solid cylindrical pipe made of wax has a radius of 2 cm and height equal to 14 cm. It is melted and recast into a solid prism of base area $16c{m}^2.$ What will be the height of the prism?

Q.

The base of a prism is in the form of an equilateral triangle of perimeter 12 cm. The height of the prism is 8 cm. What is the volume of of the prism?

1. $32\sqrt{3}c{m}^3$
   

2. $16\sqrt{2}c{m}^3$
   

3. $32\sqrt{2}c{m}^3$
   

4. $16\sqrt{3}c{m}^3$

Q. The base of a prism is a regular hexagon. If every edge of the prism measures $1$ meter, then the volume of the prism is :

1. $\frac{3\sqrt{2}}{2}{m}^3$
2. $\frac{3\sqrt{3}}{2}{m}^3$
3. $\frac{6\sqrt{2}}{2}{m}^3$
4. $\frac{5\sqrt{3}}{2}{m}^3$

Q. If all the edges of a rectangular prism are doubled and its shape is left unchanged, then the volumes increases

1. $2$ times
2. $3$ times
3. $4$ times
4. $8$ times

Q. What is the volume (in $c{m}^3$) of the prism whose base is a hexagon of side 6 cm and height $12\sqrt{3}$ cm?

1. $1944\sqrt{3}$
2. 1944
3. $1654\sqrt{3}$
4. 1654

Q. Which of the following is required to find the total surface area of a prism?

1. Perimeter of the base
2. Width
3. Height
4. Base area

Q.

Adding the following gives the total surface area of a prism.

a)Area of the top surface

b)Area of the lateral surfaces.

c) Area of the base.

1. True

2. False

Q. What is the amount of space on the outside of a triangular prism called?

1. Volume
2. Surface Area
3. Height
4. Base

Q.

Two identical prisms with triangles as base are joined to form a rectangular prism as shown below.

What is the total surface area of the rectangular prism?

Q.

The base of a prism is a rectangle having sides 5 cm and 12 cm respectively. The height of the prism is 18 cm. It is split vertically along the diagonal of the base into two triangular prisms. What is the total surface area of each of the triangular prism?

1. $400c{m}^2$
2. $600c{m}^2$
3. $800c{m}^2$
4. $1200c{m}^2$

Q.

A rectangular plot of land measures 45m x 30m. A boundary wall of height 2.4 m is built all around the plot at a distance of 1 m from the plot. Find the area of the inner surface of the boundary wall.

Q.

What is the height of a square based prism whose base edge is 6cms and lateral surface surface area is 288sq.cms

Q.

A solid cylindrical pipe made of wax has a radius of 2 cm and height equal to 14 cm. It is melted and recast into a solid prism of base area $16c{m}^2.$ What will be the height of the prism?

1. 11 cm
2. 12 cm
3. 22 cm
4. 21 cm

Q.

The base area of a prism is $40c{m}^2$. What would be the height of the prism if its volume = $200c{m}^3$ ?

1. 7 cm

2. 6.3 cm

3. 5 cm

4. 4 cm