Question

36.
A solid toy is in the form of a hemisphere surmounted by a right circular
cone of same radius. The height of the cone is 10 cm and the radius of the
base is 7 cm. Determine the volume of the toy. Also find the area of the
coloured sheet required to cover the toy. ​

Answer 1

Answer:

Step-by-step explanation:

VOLUME OF TOY =VOLUME OF CONE +VOLUME OF HEMISPHERE

r=7cm

h of cone=10cm

VOL. OF CONE= ⅓πr²h

=⅓x22/7x7x7x10

=1540/3cm³

VOL. OF HEMISPHERE=⅔πr³

=⅔x22/7x7x7x7

=2156/3cm³

VOLUME OF TOY =2156/3+1540/3

=3696/3

=1232cm³

l²=r²+h²=(7)²+(10)²=49+100=149

l=√149=12.2cm

AREA OF COLOURED PAPER REQUIRED=C.S.A. OF CONE + C.S.A. OF HEMISPHERE

C.S.A. OF CONE=πrl

=22/7x7x12.2

=268.4cm²

C.S.A.OF HEMISPHER=2πr²

=2x22/7x7x7

=308cm²

AREA OF REQUIRED PAPER=

=268.4+308

=576.4cm²

~~~~~||||| HOPE THIS WILL HELP YOU |||||~~~~~

Answer 2

The Volume of The Toy is 1230.88 cm³

The Area of coloured sheet required to cover the toy is 575.84 cm²

Step-by-step explanation:

Given as :

A solid toy is in the form of a hemisphere surmounted by a right circular  cone

The radius of hemisphere = r  cm

The radius of cone = R = r = 7 cm

So, The radius of hemisphere = r = 7  cm

The height of the cone = h cm

Let The volume of cone = V cubic cm

Let The Area of coloured sheet required to cover the toy = A sq cm

According to question

For hemisphere part

∵ Volume of hemisphere = $V_1$  = $\dfrac{2}{3}$  × π × radius³

i.e  $V_1$  = $\dfrac{2}{3}$  × π × r³

Or,  $V_1$  = $\dfrac{2}{3}$  × 3.14 × (7 cm)³

∴     $V_1$  = 718.013 cm³

So, The  Volume of hemisphere = $V_1$ = 718.013 cm³

Again

For conic part

∵ Volume of cone = $V_2$  = $\dfrac{1}{3}$  × π × radius² × height

i.e   $V_2$  = $\dfrac{1}{3}$  × π × r² × h

Or,  $V_2$  = $\dfrac{1}{3}$  × 3.14 × (7 cm)² × 10

∴     $V_2$  = 512.867 cm³

So, The Volume of cone = $V_2$  =  512.867 cm³

Therefor The Volume of Toy = Volume of hemisphere  + Volume of cone

i.e    V = $V_1$  + $V_2$

Or,   V =  718.013 cm³  +  512.867 cm³

∴      V = 1230.88 cm³

So,  The Volume of The Toy =  V = 1230.88 cm³

Again

The Area of coloured sheet required to cover the toy = Curved surface area of hemisphere + curved surface area of cone

i,e   A = CSA  of hemisphere + CSA of cone

Or,  A = 2 × π × radius²  + π × radius × slant height

i.e   A = 2 × 3.14 × (7 cm)²  + 3.14 × 7 cm × ( $\sqrt{h^{2}+r^{2} }$ )

Or,  A = 307.72 + 21.98  × ( $\sqrt{10^{2}+7^{2} }$ )

Or,  A = 307.72 + 21.98  × $\sqrt{149}$

Or,  A = 307.72 + 21.98  × 12.20

∴     Area = 575.84   cm²

So, The Area of coloured sheet required to cover the toy = A = 575.84   cm²

Hence, The Volume of The Toy is 1230.88 cm³

And The Area of coloured sheet required to cover the toy is 575.84 cm²  Answer