Question

the toy in a form of a cone mounted with a hemisphere of commom base of diameter 7cm if the height of the toy is 15.5,find the total surface area of a toy ​

Answer 1

$\huge\star{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}⋆$

The volume of the toy is 231 cm cube.

Total surface area of the toy is 203.5 cm square.

Step-by-step explanation:

Given : A toy is in the form of cone mounted on the hemisphere of diameter 7 cm . the total height of the tower is 14.5 cm.

To find : The volume and total surface area of the toy?

Solution :

Hemisphere of diameter 7 cm

Radius is $r=\frac{7}{2}=3.5$

Height of the toy= 14.5

Height of the cone= 14.5 - 3.5=11cm

Height of the hemisphere=3.5cm

According to question,

Volume of the toy = V(cone)+ V(hemisphere)

$V=\frac{1}{3}\pi r^2 h+\frac{4}{3}\pi r^3$  

$V=\frac{1}{3}\pi r^2[h+2r]$    

$V=\frac{1}{3}\times \frac{22}{7}\times (3.5)^2[11+2(3.5)]$  

$V=\frac{1}{3}\times \frac{22}{7}\times 3.5\times 3.5\times 18$  

$V=231$  

The volume of the toy is 231 cm cube.

$l=\sqrt{r^2+h^2}\\l=\sqrt{3.5^2+11^2}\\l=\sqrt{133.25}\\l=11.5$

Total surface of the toy = TSA(cone)+ TSA(hemisphere)

$TSA=\pi rl+2\pi r^2$

$TSA=\pi r(l+2r)$

$TSA=\frac{22}{7}\times 3.5(11.5+2(3.5))$

$TSA=\frac{22}{7}\times 3.5\times 18.5$

$TSA=203.5cm^2$

Total surface area of the toy is 203.5 cm square.