Question

Solve this please......​

Answer 1

Figure refer to attachment

Question :-

The object is made of two solids - a cube and hemisphere .The base of the figure is a cube with edge 5cm and the hemisphere fixed at the top has a diameter 4.2cm. Find the total surface area of object

To find :-

Find the total surface area of object

Solution :-

• Edge of cube = 5cm
• Diameter of hemisphere = 4.2cm
• Radius of hemisphere = 4.2/2 = 2.1cm

$\large{\blue{\boxed{\bf{\red{Method\::1}}}}}$

Applying Formula of cube and hemisphere to solve this question

Now

Total surface area of cube

= 6 × a²

= 6 × (5)² = 6 × 25 = 150cm²

Curved surface area of hemisphere

= 2πr²

= 2 × 22/7 × (2.1)²

= 27.72cm²

The surface area of object

= Total surface area of cube - base area of hemisphere + curved surface area of hemisphere

= 150 - πr² + 27.72

= 150 + 27.72 - 22/7 × (2.1)²

= 177.72 - 13.86

= 163.86cm²

$\large{\blue{\boxed{\bf{\red{Method\::2}}}}}$

Total surface area of object

= TSA of cube - base area of hemisphere + CSA of hemisphere

Putting the value of total surface area of cube

= 150 - πr² + 2πr²

= 150 + πr²

= 150 + 22/7 × (2.1)²

= 150 + 13.86

= 163.86cm²

$\purple{\boxed{\bf{\purple{Total\:surface\:area\:of\:object=163.86cm^2}}}}$

Some Formulae

• Total surface area of hemisphere = 3πr²
• Curved surface area of hemisphere = 2πr²
• Volume of hemisphere = 2/3πr³
• Volume of cube = a³
• Lateral surface area of cube = 6a²
• Total surface area of cube = 6a²