Twelve solid hemispheres of the same size are melted and recastto in a right circular cylinder of di...........

Quantitative Aptitude (CPO) Geometry

Twelve solid hemispheres of the same size are melted and recastto in a right circular cylinder of diameter 7 cm and height 28 cm.

Whatis the radius of the hemispheres?

This questions was previously asked in

SSC CPO 12th Dec 2019 Shift-2

4.5 cm

3.5 cm

3 cm

3.8 cm

- We have 12 hemispheres melted and recast into a cylinder.

- The volume of the cylinder is calculated using the formula \( V = \pi r^2 h \).

- The cylinder's diameter is 7 cm, so the radius is 3.5 cm.

- Cylinder's height is 28 cm.

- Cylinder volume = \(\pi (3.5)^2 \times 28\).

- Each hemisphere's volume is \( \frac{2}{3} \pi r^3 \).

- Total volume of 12 hemispheres = 12 \(\times \frac{2}{3} \pi r^3\).

- Equate both volumes: \(\pi (3.5)^2 \times 28 = 12 \times \frac{2}{3} \pi r^3\).

- Solve for \( r \).

- Doing the math, \( r = 3.5 \) cm.

Option:2 - 3.5 cm

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