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| = Hints for difficult problems = | | = Hints for difficult problems = |
− | Craft teacher of a school taught the students to prepare cylindrical pen holders out of card board. In a class of strength 42, if each child prepared a pen holder of radius 5 cm and height 14 cm, how much cardboard was consumed? | + | ==Mensuration== |
| + | Exercise 16.1<br>Problem 7. |
| + | |
| + | 1)Craft teacher of a school taught the students to prepare cylindrical pen holders out of card board. In a class of strength 42, if each child prepared a pen holder of radius 5 cm and height 14 cm, how much cardboard was consumed? |
| + | Statement of the problem: How much cardboard was consumed to prepare 42 cylindrical pen holders each of radius 5 cm and height 14 cm. |
| + | *Interpretation; |
| + | Case 1)Pen stand which is open on top and closed base. |
| + | Then we have to calculate Curved surface area of cylinder and area of one circle. |
| + | |
| + | *skills |
| + | visualising the cylinder into rectangle and circle |
| + | *Assumptions: |
| + | |
| + | Concepts used |
| + | #basics of circles -radius |
| + | # area of circles |
| + | # addition and multiplication of fractions |
| + | #unit of area |
| + | |
| + | knowledge to be used |
| + | #knowledge of Polygons -Rectangles |
| + | # knowledge of measurements |
| + | #Formula of CSA of cylinder |
| + | #substitution |
| + | #computing |
| + | #Value of Л |
| + | |
| + | Concepts to be taught |
| + | #basics of circles -radius |
| + | # area of circles |
| + | #relation between circumference of circle and length of rectangle in a cylinder |
| + | # addition and multiplication of fractions |
| + | #unit of area |
| + | solution: r=5cm, h=14cm, Л= |
| + | Curved surface area of cylinder and area of one circle= CSA of cylinder+area of circle |
| + | =2Лrh+ Л |
| + | = 2XX5X14+X |
| + | =440+78.5 |
| + | =518.5 |
| + | |
| + | Cardboard required to prepare 42 penstands= 42X518.5=21777 |
| + | |
| + | =2.1777 |
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| + | |
| + | Case 2:- Hollow pen stand: Pen stand which is open both the sides i.e., top and base. |
| + | Then we have to calculate Curved surface area of cylinder. |
| + | Case 3:-Pen stand which is closed both the sides i.e., top and base. |
| + | Then we have to calculate total surface area of cylinder. |
| + | |
| + | Activity |
| + | Making use of 2200 cmcardboard sheet how many hollow cylinders of radius 7 cm and height 5 cm can be prepared. |
| + | |
| + | |
| + | 2)Find the weight of a solid cone whose base is of diameter 14 cm and vertical height 51, |
| + | cm, if the material of which it is made weighs 10gm/ |
| + | |
| + | *Statement of the problem:What is the weight of a solid cone whose base is of diameter 14 cm and vertical height 51cm, if the material of which it is made weighs 10gm/ |
| + | *Interpretation; |
| + | Calculating the weight of solid cone by calculating its volume. |
| + | density of a material is given. it is related to volume and weight. |
| + | |
| + | * Assumptions: |
| + | Concepts used |
| + | #basics of circles -radius |
| + | # area of circles |
| + | # multiplication of fractions |
| + | #unit of volume,density and weight |
| + | #density |
| + | |
| + | knowledge to be used |
| + | #radius= |
| + | |
| + | #density= |
| + | # knowledge of measurements |
| + | #Formula of volume of cones |
| + | #substitution |
| + | #computing |
| + | #Value of Л |
| + | |
| + | Concepts to be taught |
| + | #density |
| + | #units conversion |
| + | |
| + | solution: |
| + | d=14cm r===7cm, h=51cm |
| + | Volume of cone=Лh |
| + | =XX7X7X51=2618 |
| + | To calculate weight of the solid cone we have to use density of the given material. |
| + | |
| + | density=10gm/ |
| + | |
| + | =Kg/ |
| + | Weight of solid cone=volumeXdensity |
| + | =2618XKg/ |
| + | =26.18Kg |
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| = Project Ideas = | | = Project Ideas = |