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Find the volume of the following cylinders.

(i) The volume of a cylinder given as =  . or given radius of cylinder = 7cm and length of cylinder = 10cm. So, we can calculate the volume of the cylinder =           (Take the value of  ) The volume of cylinder = .   (ii) Given for the Surface area =  and height = 2m . we have .

Find the volume of the following cubes

(a) with a side 4 cm             (b) with a side 1.5 m

(a) Volume of cube having side equal to 4cm will be     or    . (b) When having side length equal to 1.5m then , .

Find the volume of the following cuboids

(i) Volume of cuboid is given as: , So, Given that Length = 8cm, Breadth = 3cm, and height = 2 cm so, its volume will be = . Aslo for Given Surface area of cuboid  and height = 3 cm we can easily calculate the volume: ; So, Volume =

Find the total surface area of the following cylinders following figure

Total surface area of cylinder = 2πr (r + h) (i)  Area =                         (ii) Area =

Find the surface area of cube A and lateral surface area of cube B (Fig 11.36).

Surface area of cube A =                                        =   Lateral surface area of cube B =

Find the total surface area of the following cuboids (Fig 11.31):

(i)  Total surface area = 2 (h × l + b × h + b × l) = 2(lb + bh + hl)                                                                          (ii) Total surface area = 2 (h × l + b × h + b × l) = 2(lb + bh + hl)

(iii)    Find the area of polygon MNOPQR (Fig 11.19) if $MP = 9 cm$, $MD = 7 cm$, $MC = 6 cm$, $MB = 4 cm$$MA = 2 cm$ NA, $OC, QD$            and $RB$ are perpendiculars to diagonal MP.

the area of polygon MNOPQR  = area of MAN + area of trapezium ACON+area of  CPO + area of  MBR+area of trapezium BDQR+area of  DPQ

(ii)     Polygon ABCDE is divided into parts as shown below (Fig 11.18). Find its area if $AD = 8 cm$, $AH = 6 cm$, $AG = 4 cm$, $AF = 3 cm$                and perpendiculars $BF = 2 cm$,$CH = 3 cm$,  $EG = 2.5 cm$. Area of Polygon ABCDE = area of $\Delta AFB+...$

Area of $\Delta AFB=\frac{1}{2}\times AF\times BF=\frac{1}{2}\times 3\times 2=....$

Area of trapezium $FBCH=FH\times \frac{(BF+CH)}{2}$

$=3\times \frac{(2+3)}{2}[FH=AH-AF]$

Area of $\Delta CHD=\frac{1}{2}\times HD\times CH=.....,$  Area of $\Delta ADE=\frac{1}{2}\times AD\times GE=...$

So, the area of polygon ABCDE = ....

Area of Polygon ABCDE = area of  + area of trapezium BCHF + area of +area of

(i)    Divide the following polygons (Fig 11.17) into parts (triangles and trapezium) to find out its area.

FI is a diagonal of polygon EFGHI         NQ is a diagonal of polygon MNOPQR

(i) Area of  polygon EFGHI = area of EFI + area of quadrilateral FGHI Draw a diagonal FH  Area of  polygon EFGHI = area of EFI + area of  FGH + area of FHI Area of polygon MNOPQR = area of quadrilateral NMRQ+area of quadrilateral NOPQ  Draw diagonal NP and NR . Area of polygon MNOPQR = area of NOP+area  of NPQ +area of NMR +area of  NRQ

Find the area of these quadrilaterals (Fig 11.14).

(i) Area=   (ii) Area= (iii)Area=

1. We know that parallelogram is also a quadrilateral. Let us also split such a quadrilateral into two triangles, find their areas  and hence that of the parallelogram. Does this agree with the formula that you know already? (Fig 11.12)

This agree with the formula that we know already.

1    Find the area of the following trapeziums (Fig 11.8)

(i)

(i) Area of trapezium    (ii)   Area of trapezium

Q2.     If h = 10 cm, c = 6 cm, b = 12 cm, d = 4 cm, find the values of each of its parts separetely and add to find the area WXYZ.            Verify it by putting the values of h, a and b in the expression $\frac{h(a+b)}{2}$.

Area of trapezium WXYZ = Area of traingle with base'c'+area of rectangle +area of triangle with base 'd'                                                                                                                                                                        the area WXYZ by  the expression  . Hence,we can conclude area from given expression and calculated area is equal.

1    Nazma’s sister also has a trapezium-shaped plot. Divide it into three parts as shown (Fig 11.4). Show that the area of a trapezium

$WXYZ=h\frac{(a+b)}{2}$.

Area of trapezium WXYZ = Area of triangle with base 'c' + area of rectangle + area of triangle with base'd'                                           Taking 'h' common, we get                                                                                        Replacing                                                                                                Hence proved that the area of...

Q.2 Write the perimeter of each shape.

2.   Perimeter of shape =    perimeter of shape = =  perimeter of shape =  perimeter of shape =   perimeter of this shape cannot be calculated only with height and breadth,we need slant height or angle.

(a) Match the following figures with their respective areas in the box.

1.    Area of above shape =  =   Area of above shape =  Area of above shape =  Area of above triangle =  Area of above shape = b*h =
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