A spherical ball of lead 6 cm in radius is melted and recast into three spherical balls. The radii of two of these balls are 3 cm and 4 cm. What is the radius of the third sphere?

Area and Perimeter

1. Area of a triangle $=\frac{1}{2}\times$Base $\times$height

2. Area of a triangle

$=\sqrt{s\left(s-a\right)\left(s-b\right)(s-c),}$ where

$s=\frac{a+b+c}{2}$

3. Area of an equilateral triangle

$=\frac{\sqrt{3}}{4}\times Sid{e}^2$

4. Area of a circle $=\pi r^2$

5. Circumference of a circle $=2\pi r$

6. Area of a sector of a circle $={360}^{°}\times \pi r^2$

7. Area of a square $=Sid{e}^2$

8. Perimeter of a square $=4\times$Side

9. Perimeter of a Rectangle

$=2(length+breadth)$

Area of a Rectangle $= (length+breadth)$

10. A rhombus is a parallelogram that has all the sides equal. In a rhombus, diagonals always bisect each other.

Area $=\frac{1}{2}\times d_1\times d_2$

11. A quadrilateral whose opposite sides are parallel is called a parallelogram. Diagonals of a parallelogram bisect each other. Area $=$Base $\times$Height

12. A trapezium is a quadrilateral with only two sides parallel to each other. Area $=\frac{1}{2}$ Sum of parallel sides $\times$ Height