Question

A vessel in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.

Answer 1

Answer:

The inner surface area of the vessel is 572 cm².

Step-by-step explanation:

SOLUTION :  

Given :  

Diameter of the hemisphere = 14 cm

Radius of the hemisphere = 14/2 = 7 cm                

Total height of the vessel , H = 13 cm  

Height of the cylinder ,h = Total height of the vessel - Radius of the hemisphere

h = 13 - 7 = 6 cm

Height of the cylinder ,h = 6 cm

Now,

Inner surface area of the vessel , S = CSA of cylinder + CSA of hemisphere

= 2πrh + 2πr²  = 2πr (h + r)  

S = 2πr (h + r)  

S = 2 × 22/7 × 7 (6 + 7)

S = 44 × 13

S = 572 cm²

Hence, the inner surface area of the vessel is 572 cm².

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

$\bf\huge\textbf{\underline{\underline{According\:to\:the\:Question}}}$  

D of  hemisphere = 14 cm

Radius of hemisphere

$\bf\huge{\implies\dfrac{14}{2}}$        

= 7 cm                

$\bf\huge\bf\huge{\boxed{\bigstar{{H=13cm}}}}$

h of cylinder = 13 - 7

= 6 cm

Height of the cylinder = 6 cm

Inner surface area  

= CSA of cylinder + CSA of hemisphere

= 2πrh + 2πr²  

= 2πr (h + r)  

= 2πr (h + r)  

$\bf\huge{\implies 2\times\dfrac{22}{7}\times 7(6+7)}$  

= 44 × 13

$\bf\huge\bf\huge{\boxed{\bigstar{{572\: cm^2}}}}$