5 Mark Question

Question 15 Marks

Leonard Euler, discovered an interesting formula regarding the faces, vertices and edges of solid figures.
Count and write the faces, vertices and edges of the following figures and complete the table. From the table verify Euler’s formula, F + V = E + 2.

Answer

From the above table, F + V = E + 2 i.e. Euler’s formula is verified.

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Question 25 Marks

Find the area of the sheet required to make a cylindrical container which is open at one side and whose diameter is 28 cm and height is 20 cm . Find the approximate area of the sheet required to make a lid of height 2 cm for this container.
Given: For cylindrical container:
diameter $( d )=28 cm$, height $\left( h _1\right)=20 cm$
For cylindrical lid: height $\left(h_2\right)=2 cm$
To find: i. Surface area of the cylinder with one side open
ii. Area of sheet required to made a lid

Answer

$\text { diameter }(d)=28 cm$
$\therefore \operatorname{radius}(r)=\frac{d}{2}=\frac{28}{2}=14 cm$
i. Surface area of the cylinder with one side open = Curved
surface area + Area of a base
solution
$=2 \pi r h_1+\pi r^2$
$=\pi r\left(2 h_1+r\right)$
$=\frac{22}{7} \times 14 \times(2 \times 20+14)$
$=22 \times 2 \times(40+14)$
$=22 \times 2 \times 54$
$=2376 sq . cm$
ii. Area of sheet required to made a lid = Curved surface area of lid + Area of upper surface
$=2 \pi r h_2+\pi r^2$
$=\pi r\left(2 h_2+r\right)$
$=\frac{22}{7} \times 14 \times(2 \times 2+14)$
$=22 \times 2 \times(4+14)$
$=22 \times 2 \times 18$
$=792 \text { sq. } . cm$
$\therefore$ The area of the sheet required to make the cylindrical container is $2376 sq$. cm and the approximate area of a sheet required to make the lid is $792 sq . cm$.

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