Question

Ez.5. Base of a right prism is a rectangle, the ratio of whose length and breadth is 3:2. If the height of the prism is 12 cm and total surface area is 288 sq. cm., the volume of the prism is : (1) 291 cm3 (2) 288 cm3 (3) 290 cm3 (4) 286 cm3

11th - 12th Class

Maths

Solution

4.0 (1 ratings)

Length of base ( =3 x mathrm{cm} ) and breadth ( =2 x ) ( mathrm{cm} ) (let) Total surface area of prism = perimeter of base ( x ) height ( +2 times ) area of base ( =[2(3 x+2 x) times 12+2 times 3 x times 2 x] ) sq. ( mathrm{cm} ) ( =left(120 x+12 x^{2}right) ) sq. ( mathrm{cm} ) According to the question. ( 120 x+12 x^{2}=288 Rightarrow x^{2}+10 x=24 ) ( Rightarrow x^{2}+10 x-24=0 Rightarrow x^{2}+12 x-2 x-24=0 ) ( Rightarrow x(x+12)-2(x+12)=0 ) ( Rightarrow(x-2)(x+12)=0 ) ( Rightarrow x=2 ) because ( x eq-12 ) ( therefore ) Volume of prism ( = ) Area of base ( x ) height ( =(3 x times 2 x times 12) ) cu. ( mathrm{cm} ) ( =72 x^{2}=(72 times 2 times 2) mathrm{cu} . mathrm{cm} .=288 mathrm{cu} . mathrm{cm} )