Grade 7 / Straight prisms and cylinder 36 exercises (including 32 corrected)

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7cm1;5cm3cm F1F2F3F4 P3P4P1P2 VuedefaceVuededessusVuededroite Vue de faceVue de dessus ChingQuizz : 3 exercises available for Quizz assessment : 1. Reminders on the right blocks E.11162 Consider the parallelepiped be-low : 1 Give the volume of this rectangular prism. 2 Determine the total area of all the faces of this rectangu-lar prism. E.6587 Below is a cavalier perspective of a cube : Reproduce this cube in cavalier perspective on the space left free on the right. E.6586 Four cavalier perspective represen-tations of rectangular parallelepipeds are incompletely shown belowou : Draw the missing continuous and dashed lines to complete their cavalier perspectives. E.6588 Consider the four cubes shown be-low : and four representations in cavalier perspective of cubes : Connect each of the cubes with its cavalier perspective repre-sentation. E.7635 The figure opposite repre-sents a solid made up of four cubes : three cubes with edge length 2 cm ; one cube with edge length 4 cm . 1 Determine the volume of this solid. 2 Two views of this solid have been drawn (they are not to scale) . Draw the right view of this solid to scale . https://chingmath.fr chapExoCorrec/11162 sacados/11162 7cm1;5cm3cm chapExoCorrec/6587 sacados/6587 chapExoCorrec/6586 sacados/6586 chapExoCorrec/6588 sacados/6588 F1F2F3F4 P3P4P1P2 chapExoCorrec/7635 sacados/7635 Asie Juin 2017 5 points VuedefaceVuededessusVuededroite Vue de faceVue de dessus
ABCDEF ABCDEFGHIJKLMNOPQRSTUV Fig.2Fig.1 Fig.3Fig.4 Fig.1Fig.4Fig.2Fig.3 ABCDEFGHIJKLMNOPQRSTUVWXYZ Fig.1Fig.2Fig.3ABCDEFGHIJKLMNOPQRSTUVWXYZ 2. Straight prisms E.9060 Consider the right prism ABCDEF shown below : 1 What is the nature of the base of this right prism? 2 a How many edges does this right prism have? b How many faces does this right prism have? E.6589 Consider the two right prisms ABCDEF and GHIJKLMNOPQRSTUV shown below : 1 Specify the nature of the base of each of these right prisms. 2 Give the number of vertices, edges, and faces of each of these right prisms. E.9057 Consider the four solids below rep-resented in cavalier perspective : Which of the solids shown above are straight primes. The nature of the base of the right prisms will be specified. E.6590 Consider the four solids below : 1 For each of the solids, give the number of vertices, edges, and faces. 2 Which of the solids shown are right prisms? For these, specify the nature of the base. 3. Straight prisms: properties E.11154 Consider the three polyhedra shown below in cavalier perspective : 1 Give the nature of each of these solids. 2 For each of these solids, name a face parallel to the col-ored face. E.11181 Consider the three polyhedra shown below in cavalier perspective : For each of the edges highlighted in the figure : highlight all parallel edges ; https://chingmath.fr chapExoCorrec/9060 sacados/9060 ABCDEF chapExoCorrec/6589 sacados/6589 ABCDEFGHIJKLMNOPQRSTUV chapExoCorrec/9057 sacados/9057 Fig.2Fig.1 Fig.3Fig.4 chapExoCorrec/6590 sacados/6590 Fig.1Fig.4Fig.2Fig.3 sacados/11154 ABCDEFGHIJKLMNOPQRSTUVWXYZ chapExoCorrec/11181 sacados/11181 Fig.1Fig.2Fig.3ABCDEFGHIJKLMNOPQRSTUVWXYZ
ABCDEFGHIJ ABCDEFGHIJKLMN name one of them. 4. Straight Prism Patterns E.6601 1 Cut out the pattern below, then build the associated right prime : (We’ll leave the lines and names of the points outside the right prism) 2 Once the solid is constructed, answer the following ques-tions : a Which segment will coincide with segment [ BI ] ? b Which segment will coincide with segment [ AD ] ? c Which points will coincide with the point A ? d Which points will coincide with the point J ? E.6602 1 Cut out the pattern below, then build the associated right prime : (We’ll leave the lines and names of the points outside the right prism) 2 Once the solid is constructed, answer the following ques-tions : a Which segment will coincide with segment [ AD ] ? b Which segment will coincide with segment [ AB ] coin-cide with which other segment? c Which points will coincide with the point G ? d Which point will coincide with the point E ? https://chingmath.fr chapExoCorrec/6601 sacados/6601 ABCDEFGHIJ chapExoCorrec/6602 sacados/6602 ABCDEFGHIJKLMN
ABCDEFGHIJABCDEFGHIJKLMN ABCDEFGHIJKLMNOPQRSUVWXY12 ABCDEF 8m12m2m E.6591 We consider the two patterns below : These two patterns allow us to construct a right prism. 1 a Specify the nature of the base of each of these right prisms. b For each of these right prisms, of what natures are the faces of the right prism? 2 For each of the solids constructed from these two pat-terns, answer the following questions : a With which segment will [ EF ] coincide? b With which points will the point J coincide? E.6603 Justify that the two figures below are not the patterns of right prisms : 5. Volume of straight prisms E.6451 Consider the right prism ABCDEF shown below : 1 What is the nature of the base of this right prism? 2 a How many edges does this right prism have? b How many faces does this right prism have? 3 Furthermore, the triangle ABC is right-angled at C and we have the following measures : AB = 7.8 cm ; AC = 3 cm ; BC = 7.2 cm ; AD = 3 cm Determine the volume of the right prism ABCDEF . E.9113 In order to build his swimming pool, Oumar dug a hole in his garden in the shape of a right paving stone and whose dimensions are: L = 12 m ; ‘ = 8 m ; h = 2 m It builds walls on the side faces with a thickness of 30 cm as well as a floor also with a thickness of 30 cm . Determine the volume of concrete required for this construc-tion. 6. Cylinder pattern E.6605 Below is the pattern of a cylinder: https://chingmath.fr chapExoCorrec/6591 sacados/6591 ABCDEFGHIJABCDEFGHIJKLMN chapExoCorrec/6603 sacados/6603 ABCDEFGHIJKLMNOPQRSUVWXY12 chapExoCorrec/6451 sacados/6451 ABCDEF chapExoCorrec/9113 sacados/9113 8m12m2m chapExoCorrec/6605 sacados/6605
6cm3cm 3cm2cm Cut out and build the cylinder from this pattern. E.6606 Below is the pattern for a cylinder: Determine the total surface area of the cylinder. Indication : we will use : ı ≈ 3.14 lengths will be rounded to the nearest tenth of a mil-limeter. Areas will be rounded to the nearest square millimeter. E.6607 Below is the pattern for a cylinder: Determine the total surface area of this cylinder. Note: Use the approximate value ı ≈ 3.14 Give the result to the nearest square millimeter 7. Volume of cylinders E.9061 To build a well in his garden, M mme Martin needs to buy concrete. Using the characteristics of the cylinder, determine the vol- ume of concrete needed to build this well, rounded to the nearest cubic centimeter. https://chingmath.fr chapExoCorrec/6606 sacados/6606 6cm3cm chapExoCorrec/6607 sacados/6607 3cm2cm chapExoCorrec/9061 sacados/9061
4cm2cm3cm 2cm2cm4cm ABCDEFGH3;2cm6cm5;1cm Characteristics of a cylinder : inner diameter : 90 cm outer diameter : 101 cm height : 50 cm Reminder : cylinder volume = ı × radius × radius × height Indication : we will use : ı ≈ 3 ; 14 E.7960 A macaron consists of two cookies and a layer of cream. This layer of cream can be likened to a cylinder with radius 20 mm and height 5 mm . 1 Check that the volume of cream contained in a macaron is 2 000 ı mm 3 . 2 Alexis has 30 c‘ of cream in his bowl. How many macarons can he make? Reminder : 1 ‘ =1 dm 3 Hint: we will use ı ≈ 3.1416 8. Volumes of the right block E.5589 Determine the volume of the two parallelepipeds below : a b E.7890 Consider the right-handed paving stone ABCDEFGH shown below whose measurements are known as follows : HG = 6 cm ; FG = 3.2 cm ; FB = 5.1 cm Determine the volume of this right block expressed in cm 3 . 9. Volume conversions E.2612 In the table below, for each row, re-trieve the volume value on the left and convert it using the unit shown on the right : km 3 hm 3 dam 3 m 3 dm 3 cm 3 mm 3 312 m 3 . . . dm 3 0 ; 32 dm 3 . . . m 3 350 mm 3 . . . m 3 25 km 3 . . . m 3 Recall the equality : 1 ‘ =1 dm 3 E.11231 Perform the following volume conver-sions : km 3 hm 3 dam 3 um 3 dm 3 cm 3 mm 3 17 m 3 dm 3 3 ; 3 dam 3 hm 3 92 mm 3 cm 3 0 ; 023 m 3 cm 3 E.10539 Copy and perform the following con-versions : a 1 200 cm 2 = : : : : : : dam 2 b 0.045 km 3 = : : : : : : dam 3 c 2.1 dm 3 = : : : : : : m 3 d 75.2 dam 3 = : : : : : : m 3 e 0.004 75 hm 3 = : : : : : : m 3 f 35 dm 3 = : : : : : : m 3 E.11227 Perform conversions : a 25 m 3 en dm 3 b 35 mm 3 en cm 3 c 78 m 3 en dam 3 d 193 dm 3 en dam 3 E.11228 Perform conversions : a 0 ; 13 cm 3 en mm 3 b 2 ; 475 m 3 en cm 3 c 41 ; 3 mm 3 en cm 3 d 102 ; 3 m 3 en dam 3 E.11229 Fill in the missing units : a 1 ; 13 m 3 = 1 130 : : : b 0 ; 03 hm 3 = 30 000 : : : c 457 ; 1 mm 3 = 0 ; 457 1 : : : d 52 000 m 3 = 0 ; 52 : : : https://chingmath.fr chapExoCorrec/7960 sacados/7960 chapExoCorrec/5589 sacados/5589 4cm2cm3cm 2cm2cm4cm chapExoCorrec/7890 sacados/7890 ABCDEFGH3;2cm6cm5;1cm chapExoCorrec/2612 sacados/2612 chapExoCorrec/11231 sacados/11231 chapExoCorrec/10539 sacados/10539 sacados/11227 sacados/11228 sacados/11229
1dm1cm arrièredroiteface avantgauche 10. Volume conversions with liters E.10537 Perform the following length con-versions : k‘ h‘ da‘ ‘ d‘ c‘ m‘ 24 ; 63 ‘ d‘ 24 m‘ h‘ 0 ; 64 da‘ ‘ 87 h‘ ‘ E.11230 In the table below, for each row, retrieve the volume value on the left and convert it using the unit shown on the right : km 3 hm 3 dam 3 m 3 dm 3 cm 3 mm 3 2 ‘ . . . m 3 33 c‘ . . . cm 3 25 dam 3 . . . h‘ 150 cm 3 . . . ‘ Recall the equality : 1 ‘ =1 dm 3 11. Introduction to changing units E.10538 Two cubes are shown below : the first with side 1 dm and the second with 1 cm . How many cubic centimeters does the cube with side 1 dm contain. 12. Unclassified exercises E.7889 We stacked and glued 6 cubes of 4 cm edge and a right prism obtained by cutting a cube in two equal parts by one of its diagonals. Below is given the representation of this solid (the views are given as a guide) Calculate the volume in cm 3 of the solid. https://chingmath.fr chapExoCorrec/10537 sacados/10537 chapExoCorrec/11230 sacados/11230 chapExoCorrec/10538 sacados/10538 1dm1cm chapExoCorrec/7889 sacados/7889 arrièredroiteface avantgauche
arrièredroiteface avantgauche ABCDEF E.843 We have stacked and glued 6 cubes of 4 cm edge and a right prism so as to obtain the solid shown below. The height of the prism is equal to half the edge of the cubes. 1 Draw a full-scale view of the back of the solid. 2 Calculate the volume in cm 3 of the solid. 3 Study of the right prism. a We name this prism ABCDEF , as in the figure below : What is the nature of the base of this right prism? Justify your answer. b Verify by calculations that the length AC =4 2 cm . c Deduce the exact value of the area of the ACFD face. Give the rounding to the nearest mm 2 . E.10542 Consider the solid below formed by two cubes : the larger cube has side 8 cm , the side of the second cube measures half a side of the first cube. 1 Determine the volume of this solid. 2 Determine the area of the outer surface of this solid. https://chingmath.fr chapExoCorrec/843 sacados/843 Amerique du Nord Juin 2011 arrièredroiteface avantgauche ABCDEF chapExoCorrec/10542 sacados/10542