1 in a 20-20 cricket match a batsman has hit boundary 7 times in 20 balls ,he has played - Maths - Surface Areas and Volumes

Question

1 in a 20-20 cricket match a batsman has hit boundary 7 times in
20 balls ,he has played so far what is the chance that next
ball
i) will also hit a boundary ? ii) will not cross the fence?
2) the sum of length, breadth and height of cuboid is 19cm also
length of its diagonal is 11cm what is the surface area of the
cuboid? [(l+b+h)^2 = (digonal)^2 + TSA]

Ankush Jain · Accepted Answer

1) Given, in the match a batsman hits the boundary 7 times in 20 balls a) probability of hitting boundary in next ball $= \frac{f a v o u r a b l e n u m b e r o f o u t c o m e s}{t o t a l n u m b e r o f o u t c o m e s} = \frac{7}{20}$ b) probability that the ball will not cross the fence = 1 - probability that the ball will cross the fence or he hits a boundary $1 - \frac{7}{20} = \frac{13}{20}$ 2) Given, the sum of length, breadth and height of cuboid =19 cm â‡’ l + b + h = 19 cm Again, length of its diagonal = 11cm $\Rightarrow \sqrt{l^{2} + b^{2} + h^{2}} = 11 \Rightarrow l^{2} + b^{2} + h^{2} = 11^{2} [o n s q u a r in g b o t h s i d e s] \Rightarrow l^{2} + b^{2} + h^{2} = 121 \Rightarrow (l + b + h)^{2} - 2 (l b + b h + h l) = 121 [u \sin g : (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + a c)] \Rightarrow (19)^{2} - 2 (l b + b h + h l) = 121 \Rightarrow 361 - 121 = 2 (l b + b h + h l) \Rightarrow 2 (l b + b h + h l) = 240 c m^{2} \Rightarrow T S A o f c u b o i d = 240 c m^{2}$