Question

A toy is in the shape of a solid cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 21 cm and 40 cm respectively, and the height of cone is 15 cm, then find the total surface area of the toy. [π = 3.14, be taken]

Answer 1

d of sphere is 21cm

r of sphere is 10.5cm

r of cone is 3.5cm

h of cone is 3cm

no. of cones = v of sphere / v of cone

no.of cones = 4/3 pi r cube/1/3 pi r square h

=> 4/3 *22/7 *10.5 *10.5 *10.5 = 1/3 *22/7 *3.5 *3.5 *3

=> 4851 cm cube = 38.5 cm cube

no of cones = 4851 cm cube / 38.5 cm cube

no of cones =126 ans..

Answer 2

Answer:

The correct answer is $5463.6cm^{2}$.

Step-by-step explanation:

Given:

If the height and diameter of the cylindrical are 21 cm and 40 cm respectively, and the height of the cone is 15 cm.

To find:

The total surface area of the toy.

Step 1

Radius$= Diameter/2$

Radius $=\frac{40}{2}$

$=20cm$

Height of cylinder$=21cm$

Height of cone $=15cm$

Slant height of the cone, $l=\sqrt{h^{2}+ r^{2} }$

$l=\sqrt{(15)^{2}+ (20)^{2} }$

$l=\sqrt{225+ 400 }$

$=\sqrt{625}$

$=25cm$

Slant height of the cone $=25cm$

Step 2

Total surface area of toy = Curved surface area of cone + Curved Surface                           area of cylinder + Area of the bottom part

Total surface area $= \pi \mathrm{rl}+2 \pi \mathrm{rhcyl}+ \pi \mathrm{r^{2} }$

$=3.14[20 * 25 + 2 *20 * 21 + 20 *20]$  

$=3.14[1740]$

$=5463.6cm^{2}$

Therefore, total surface area of toy $=5463.6cm^{2}$.

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