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

Explain the relationship between the area of cross-sections of a three-dimensional shape and its total volume.

6. \( A D, B E \) and \( C F \) are the three altitudes of \( \triangle A B C \). Show that \( \begin{array}{ll}\text { (i) Perimeter of triangle } A B C>2 A D & \text { (ii) Perimeter of triangle } A B C>2 B E \\ \text { (iii) Perimeter of triangle } A B C>2 C F & \text { (Perimeter of triangle } A B C)>2(A D+B E+C F)\end{array} \)

Soit \( A B C \) un triangle. Eet \( F \) deux points tel que: \( \overrightarrow{B E}=2 \overrightarrow{A C} \quad \) et \( \overrightarrow{C F}=\frac{1}{2} \overrightarrow{A B} \) 1) Construire les points \( E \) et \( F \). 2) Montrer que : \( \overrightarrow{A E}=\overrightarrow{A B}+2 \overrightarrow{A C} \quad \) et \( \overrightarrow{A F}=\frac{1}{2} \overrightarrow{A B}+\overrightarrow{A C} \)

e) La somma e la differenza delle diagonali di un rombo misurano 126 cm e 18 cm . Calcola la misura del raggio della circonferenza inscritta nel rombo.

102. The sides of right-angled triangle, containing \( \sqrt{ } 3 \) the right-angle, are \( 5 x \mathrm{~cm} \) and \( (3 x-1) \mathrm{cm} \). Calculate the length of the hypotenuse of the triangle, if its area is \( 60 \mathrm{~cm}^{2} \).