Volume of Triangular Prisms

Q.

Emily convinced her mom to buy a giant box of her favorite cereal. Her mom doesnt think the box will fit on their shelf. The volume of the box is $10,000c{m}^3$ The base of the box is $25cm$ by $10cm$ . How tall is the box of cereal?

Q.

Find the volume of the described solid $S$.
A pyramid with height $h$ and base an equilateral triangle with side $a$ (a tetrahedron).

Q.

Two cubes have volumes in the ratio $1:64$.

The ratio of the area of a face of first cube to that of the other is

1. $1:4$

2. $1:8$

3. $1:16$

4. $1:32$

Q.

Do the two solids have the same volume? Explain.

Q.

Find the volume of triangular prism whose base area is $20c{m}^2$ and height is 15 cm.

1. $250c{m}^3$

2. $300c{m}^3$

3. $200c{m}^3$

4. $350c{m}^3$

Q.

The base of a prism is an equilateral triangle of perimeter 30 cm. The height of the prism is 10 cm. Find the volume of the prism.

1. 100 $\sqrt{3}c{m}^3$
2. 250 $\sqrt{3}c{m}^3$
3. 200 $\sqrt{3}c{m}^3$
4. 175 $\sqrt{3}c{m}^3$

Q.

The base of a prism is a rectangle of sides 6 cm and 8 cm and its height is 12 cm. It is split vertically along the diagonal of the base into two triangular prisms. What is the lateral surface of each of these triangular prisms?

1. $292c{m}^2$
   

2. $280c{m}^2$
   

3. $284c{m}^2$
   

4. $288c{m}^2$

Q. The bases of a right prism is a hexagon with one of each side equal to $6cm$. The bases are $12cm$ apart. What is the volume of the right prism (in ${cm}^3$)?

1. $1211.6$
2. $2211.7$
3. $1212.5$
4. $1122.4$

Q.

A prism has a base as a right angled triangle with base 6 cm and altitude 8 cm. It is filled with water to a certain height. If a solid cube of side 6 cm is immersed in the prism, the height by which the water level will rise will be equal to ____.

1. 3 cm
2. 6 cm
3. 9 cm
4. 12 cm

Q. The capacity of the rectangular prism or cuboid is

1. $lbw$
2. $lb$
3. $bh$
4. $lw$

Q. The base of a prism is triangular in shape with sides $3cm,4cm$ and $5cm$. Find the volume of the prism if its height is $10cm$.

Q. A prism has an equilateral triangular base. The side of the triangle is 8 cm, and the height of the prism is 14 cm. The volume of the prism is cc.

1. $204\sqrt{3}$
2. $234\sqrt{3}$
3. $224\sqrt{3}$

Q. Find the volume (in ${cm}^3$) of this right triangular prism.

1. $60$
2. $90$
3. $120$
4. $150$

Q. Determine the volume (in ${ft}^3$) of a right truncated triangular prism with the following definitions:
Let the corners of the triangular base be defined by $A,B$ and $C$.
The length of $AB=10ft.,BC=9ft.$ and $CA=12ft$.
The sides $A,B$ and $C$ are perpendicular to the triangular base and have the height of $8.6ft.,7.1ft.$ and $5.5ft.$ respectively.

Q. The base of a right prism is a hexagon with one side $6cm$ long. If the volume of the prism is $450cc$, how far (in cm) apart are the bases?

1. $3,56$
2. $5.74$
3. $4.11$
4. $4.81$

Q. Find the volume of a regular hexagonal based prism with base side $4$cm and height $10$cm.

Q. A sandbox shaped like a right triangular prism has a base of $2.6m$ and a height of $1.7m$. If the sand in the box is $0.3m$ deep, how many full cubic metres of sand do you need to buy?

Q. If the volume of a square-based prism is $250c{m}^2$ and height is $10$cm, find the total surface area.

Q.

The faces of a regular triangular pyramid are:

1. Congruent

2. Similar

3. Congruent but not similar

4. None of these

Q. The base edge of a regular pentagonal prism is $6cm$ and its bases are $12cm$ apart. Find its volume in $cu.cm$.

1. $743.22$
2. $786.89$
3. $842.12$
4. $567.45$

Q.

A triangular prism has a base of an equilateral triangle of side 3.5 cm. Water is filled till the height of 10 cm in the prism. If a small ice cube of side 2 cm is put inside it, the water level rises to different height. What is the new height?

1. 11.5 cm
2. 10.5 cm
3. 12.5 cm
4. 13.5 cm

Q. The base edge of a regular hexagonal prism is $6$ cm and its bases are $12$ cm apart. Find its volume in cu.cm

1. $1896.37$
2. $1058.45$
3. $1122.37$
4. $1563.45$

Q. Find the volume of square based right prism whose base is $9$cm and height is $12$cm.

Q. The volume of a right triangular prism $ABC{A}_1{B}_1{C}_1$ is equal to $3$. If the position vectors of the vertices of the base $ABC$ are $A(1,0,1),B(2,0,0)$ and $C(0,1,0)$, then position vectors of the vertex $A_1$ can be

1. $(2,2,2)$
2. $(0,2,0)$
3. $(0,-2,2)$
4. $(0,-2,0)$

Q. How many faces does a cuboid have?

1. 4
2. 8
3. 6
4. 5

Q. The area of the base of a right circular prism in $50c{m}^3$ and its height is 8 cm .What is its volume ?

Q. The base of a right prism is an equilateral triangle of side $6$m. If its volume is $81\sqrt{3}{m}^3$, find the height of the prism.

Q.

A prism has a base as a right angled triangle with base 6 cm and altitude 8 cm. It is filled with water to a certain height. If a solid cube of side 6 cm is immersed in the prism, the height by which the water level will rise will be equal to ____.

1. 3 cm
2. 6 cm
3. 9 cm
4. 12 cm

Q. The base of the prism is an equilateral triangle of side $8cm$ and height $12cm$. Find its volume

1. $220.13cc$
2. $332.554cc$
3. $250cc$
4. $150cc$

Q. The base of a prism is a right angle triangle and the two sides containing the right angle are $8$cm and $15$cm. If its height is $20$cm, then the volume of the prism is ________.

1. $160c{m}^3$
2. $300c{m}^3$
3. $600c{m}^3$
4. $1200c{m}^3$