The **cone of revolution and the pyramid** through corrected 4th grade math exercises. Students will need to know their volume formulas and also know how to convert quantities. Develop skills in representing the solid in cavalier perspective and in space geometry.To draw a cone pyramid pattern, you must first draw a cone on a sheet of paper. Next, you can draw a vertical line through the highest point of the cone, called the apex. This line will represent the axis of symmetry of the pyramid. Next, you can draw a series of lines parallel to the base of the cone, equally spaced, to represent the different faces of the pyramid. The correction is available to allow the student to correct himself and fill in his gaps in order to progress on the cones and pyramids in eighth grade.

Exercise 1:

A pyramid has a base of 6 cm square and a height of 34 cm. Calculate its volume.

Exercise 2:

A cone has a base radius of 7 cm and a height of 9 cm. Calculate its volume, then give an approximate value to the nearest hundredth of a ^{cm3}.

Exercise 3:

A pyramid has for base a triangle ABC rectangle in B such that AB = 4.5 cm, AC = 7.5 cm and BC = 6 cm. Its height is 7 cm. Calculate its volume.

Exercise 4:

A pyramid has for base a parallelogram ABCD such that AB = 4 cm, AD = 4.5 cm, and AH = 4 cm ( H is the intersection point of the perpendicular to ( DC ) passing through A ). The height of this pyramid is 8 cm. Calculate the volume of this pyramid.

Exercise 5:

A cone has a volume of 18 cm3^{. } Its height is 5 cm. What is the radius of its base circle? (we will give the exact value, then the value approached to the hundredth)

Exercise 6:

The volume of a pyramid is 63 ^{cm3} and its base is a square of 5 cm side. How high is it?

Exercise 7:

A pyramid has for base a triangle DEF rectangular in E . We know that its height (at the pyramid) is 7 cm, that DE = 4 cm, and that its volume is 0.05 L.

- a. Calculate EF .
- b. Deduct DF .

Exercise 8:

A pyramid has a rhombus base with diagonals of 7 and 5 cm respectively. Its height is 12 cm. What is its volume in ^{dm3}?

Exercise 9:

Convert the following volume in cm3^{: }

a. 6 ^{dm3}.

b. 0.9 daL.

c. 45 ^{mm3}.

d. 0,092^{m3}.

e. 0.039 hL.

f. 0.000756 ^{dam3}

g. 67cL.

Exercise 10:

A pyramid has for base an isosceles trapezoid of height 4 cm, small base 5 cm, large base 7 cm. The height of this pyramid is 14 cm. What is its volume?

Exercise 11:

A pyramid with a rectangular base, regular, has the dimensions :

length of the base: 5 cm.

Width of the base: 4 cm.

Height of the pyramid: 6 cm.

1 . Calculate the length of a diagonal of the base to the nearest hundredth of a cm.

2. Deduce the length of an edge of a triangle of the pyramid to the nearest hundredth of a cm.

3. Calculate the volume of this pyramid.

4. Construct the pattern of this pyramid.

Exercise 12:

A regular pyramid with a square base has dimensions :

- Side of the square: 4 cm.
- Length of a side edge : 8 cm.

Draw a pattern of this pyramid.

Exercise 13:

A regular pyramid with a square base has dimensions :

- Side of the square: 6 cm.
- Height: 8 cm.

Draw a pattern of this pyramid.

Exercise 14:

A cone of revolution has for generatrix a segment of length 7 cm, and for base a disk of radius 4 cm. Draw a pattern of this cone after calculating the angle of the angular sector (recall: this angle is proportional to the length of its arc, which is equal to the perimeter of the base disk)

Exercise 15:

A pyramid has for base a rectangle of dimensions 6 by 4 cm, and for height 8 cm. The foot of its height passes through the intersection of the two diagonals of the rectangle.

1. Draw a pattern of this pyramid.

2. What is the volume of this pyramid?

3. What is the lateral area of this pyramid?

Exercise 16:

A pyramid has a rhombus base whose diagonals have dimensions of 8 and 5 cm. The height of this pyramid is 4 cm.

1. Draw a pattern of this pyramid.

2. What is the volume of this pyramid?

Exercise 17:

A pyramid has a square base with a diagonal of 6 cm. The height of this pyramid is 5 cm.

Draw a pattern of this pyramid.

Exercise 18:

A cone of revolution has a height of 6 cm, and a base radius of 4 cm.

- 1. What is its volume?
- 2. Draw a pattern of this cone, after having calculated the length of the generatrix and the angle of the angular sector.

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