Question

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Answer 1

➟ Question :-

A soild is made up of a cube and a hemisphere attached on its top, as shown in the figure. Each edge of the cube measures 5 cm and the hemisphere has a diameter of 4.2 cm. Find the total area to be painted.

➟ Given :-

$⟶$edge of the cube is 5cm

$⟶$diameter of hemisphere is 2.1cm

➟ To find :-

$⟶$the total area to be painted

➟ Formula required :-

$⟶$total surface area of cube=6a²

$⟶$base area of hemisphere =πr²

$⟶$curved surface area of hemisphere =2πr²

➟ Solution :-

⟶ Edge of the cube, a = 5 cm,

⟶ Radius of the hemisphere, r = $( \frac{4.2}{2} ) = 2.1$cm

$⟹$Total area to be painted = total surface area of the cube -base area of the hemisphere + curved surface area of the hemisphere

$⟹$6a² - πr² + 2πr² = 6a² + πr²

$⟹ (6 \times 5 \times 5 + \frac{22}{7} \times 21 \times 21)$

$⟹$(150 + 13.86)cm²

$⟹$$\boxed{\sf 163.86 cm²}$

Hence total area to be painted is 163.86cm²