Question

11. A boy has a toy which has shape as shown below
7 cm
3.5 cm
The height of the conical part is equal to radius of the base of toy.
On the basis of above information answer the following question:
(i) Find the entire height of the toy.
(ii) Find the surface area of cylindrical part in 2
.
(iii) Find the surface area of conical part in 2
.
(iv) Find total surface area of toy in 2

Answer 1

Answer:

Step-by-step explanation:

Height of the toy = 15.5 cm.

Radius of the hemisphere = 3.5 cm, as shown in the above figure.

From the figure we can say that the radius of cone = radius of the hemisphere = 3.5 cm

Height of the cone (h) = height of the toy – radius of the hemisphere.

So, the height of the cone (h) = 15.5 – 3.5 = 12 cm.

Now as we know that the slant height of the cone is given as

Slant height (l) = (height of the cone)2+(radius of the cone)2−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√

Now substitute the values we have,

Slant height (l) = (12)2+(3.5)2−−−−−−−−−−−√=144+12.25−−−−−−−−−√=156.25−−−−−√=12.5cm.

Now as we know that the lateral surface area (LSA) of the cone is given as,

LSA = πrl square units, where r and l are the radius and the slant height of the cone.

⇒LSA=227(3.5)(12.5)=137.5 cm2.

Now as we know that the curved surface area (CSA) of the hemisphere is 2πr2 where r is the radius of the hemisphere.

Therefore, CSA = 2(227)(3.5)2=77 cm2.

So, the total surface area of the toy is the sum of the lateral surface area of the cone and the curved surface area of the hemisphere.

Therefore, the total surface area (TSA) of the toy = LSA of the cone + CSA of the hemisphere.

Therefore, the total surface area (TSA) of the toy = 137.5 + 77 = 214.5 cm2.

Now as we know that the volume of the cone = 13πr2h cubic units, where r and h are the radius and the height of the cone.

And the volume of the hemisphere = 23πr3 cubic cm, where r is the radius of the hemisphere.

So the total volume of the toy = volume of the cone + volume of the hemisphere.

So the total volume of the toy = 13πr2h + 23πr3 cm3.

Now substitute the values we have,

So the total volume of the toy is,

⇒13(227)(3.5)2(12)+23(227)(3.5)3=154+89.833=243.83 cm3.

So this is the required answer.