Relation between Height, Slant Height & Base Edge

Q. The slant height of a pyramid is the height of the pyramid.

1. less than
2. greater than
3. equal to

Q.

What is the ratio between the base edge, slant height and height of a square pyramid having equal edges?

1. 1:2:2

2. $\sqrt{2}:2:3$

3. $2:\sqrt{3}:\sqrt{2}$

4. 1:1:1

Q.

What is the slant height of a square pyramid of base perimeter 80 centimeters and volume 1600 cubic centimeters?

1. $61\sqrt{2}$

2. 61

3. 122

4. 244

Q.

In any square pyramid, the squares of the height, slant height and lateral edge are in arithmetic sequence.

1. True

2. False

Q. Question 2 (iii)
Consider the following parallelograms. Find the values of the unknowns x, y, z
(iii)

Q.

If the slant height of a pyramid is 5 m and its base edge is 6 m long, then find the height of the pyramid.

1. 4 m

2. 3 m

3. 5 m

4. 6 m

Q.

All edges of a square pyramid are of equal lengths. If the length of the base edge is $40cm$, what is the slant height?

1. 1600

2. $20\sqrt{3}$

3. $10\sqrt{3}$

4. 1200

Q.

The measurements of the lateral surface of a square pyramid are shown in the figure. What are the slant height and the base edge of the pyramid respectively?

1. $10\sqrt{3},20$

2. $20,10\sqrt{3}$

3. 10, 20

4. $10\sqrt{3},10$

Q. Which of the following are true?

1. The slant height of square pyramid= $\sqrt{(Lateraledge{)}^2-(Halfthebaseedge{)}^2}$
2. Lateral edge of the square pyramid = $\sqrt{slantheightofsquarepyramid{)}^2-(Halfthebaseedge{)}^2}$
3. The slant height of square pyramid=$\sqrt{(Heightofthepyramid{)}^2+(Halfthebaseedge{)}^2}$
   
4. The height of the pyramid = $\sqrt{(Theslantheightofsquarepyramid{)}^2+(Halfthebaseedge{)}^2}$

Q.

If a square pyramid of base 12 cm and height 5 cm is to be made, then its triangular faces are all equilateral triangles with side 12 cm.

1. 110

2. 100

Q.

Find the volume and surface area of a pyramid with a triangular base with each edge 6 cm and a height of 10 cm. [4 MARKS]

Q. Find lateral surface area and volume for a square pyramid with base edge length 24 cm, and height 16 cm.

Q.

In any square pyramid, the squares of the height, slant height and lateral edge are in arithmetic sequence.

1. True

2. False

Q.

A sector with central angle 80⁰ is rolled into a cone. The ratio of the radius and slant height is:

1. 211

2. 112

3. 221

4. 121

Q. Pick the equation that relates the base radius, height and slant height of a cone from the following.

1. $Heigh{t}^2+(SlantHeight{)}^2=(Baseradius{)}^2$
2. $Baseradiu{s}^2+(SlantHeight{)}^2=(Height{)}^2$
3. $Heigh{t}^2+(BaseRadius{)}^2=(SlantHeight{)}^2$
4. $(SlantHeight{)}^2-(BaseRadius{)}^2=Heigh{t}^2$

Q.

Sujitha had made a square pyramid but one of the triangular faces went missing. Her friend said she will help her. What should be the slant height of the pyramid if it has a base of 16 cm and height 15 cm?

1. 10.5

2. 5.25

3. 5.75

4. 11.5

Q.

A square pyramid covers an area of $400m^2$ on the ground and height of the pyramid is 10 m. Then find its total surface area of the pyramid

1. $200(1+\sqrt{2})m^2$

2. $400(1+\sqrt{2})m^2$

3. $400(1+\sqrt{6})m^2$

4. $200(1+\sqrt{6})m^2$

Q.

Find the volume of the square pyramid, if one of the triangular faces is given below.

1. $1200c{m}^3$

2. $1280c{m}^3$

3. $1250c{m}^3$

4. $1220c{m}^3$

Q. A conical tent is $10$m high and the radius of its base is $24$m. Find slant height of the tent.

Q. What is the relations between height, radius and slant height of a cone ?

Q.

The Great Pyramid is approximately $150\mathrm{m}$.

Its height is about $1.5$ segments long.

Show your work like this. $(1.5\times 100\mathrm{m}=150\mathrm{m})$ for the height of the Great Pyramid.

What is the approximate height for the rest of the tall buildings, Eiffel Tower, Willis Tower, CN Tower, and Burj Khalifa Tower.

Q. How to find a sloping edge of a rectangular based pyramid? The rectangular based has length 4.8m and width 3m and the height of the pyramid is 4m .

Q. Find the volume of the square pyramid, if one the triangular faces is given below.

Q. If height of a cone is $h$, its slant height is $l$, then radius of it's base will be:

1. $\sqrt{l+h}$
2. $\sqrt{l-h}$
3. $\sqrt{h^2-l^2}$
4. $\sqrt{l^2-h^2}$

Q. The measurements of the lateral surface of a square pyramid are shown in the figure. What are the slant height and the base edge of the pyramid respectively?