Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
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 [SSC-CHSL (10+2) Exam, 2015]
(a)$291 \mathrm{cm}^{3}$
(b)$288 \mathrm{cm}^{3}$
(c)$290 \mathrm{cm}^{3}$
(d)$286 \mathrm{cm}^{3}$
Answer
Answer (as printed): B
Explanation
Let the length of base be $3 a$ cm and breadth be $2 a \mathrm{cm}$ Total surface area of prism $$=[\text { perimeter of base } \text { × } \text { height }]+[2 \times \text { area of base }] \begin{aligned} & =[2(3 a+2 a) \times 12+2 \times 3 a \times 2 a] \text { sq. } \mathrm{cm} . \\ & =\left(120 a+12 a^{2}\right) \text { sq. } \mathrm{cm} . \end{aligned}$$ According to the question, $$120 a+12 a^{2}=288 \begin{aligned} & \Rightarrow a^{2}+10 a=24 \\ & \Rightarrow a^{2}+10 a-24=0 \\ & \Rightarrow a^{2}+12 a-2 a-24=0 \\ & \Rightarrow a(a+12)-2(a+12)=0 \\ & \Rightarrow(a-2)(a+2)=0 \\ & \Rightarrow a=2 \text { because } a \neq-12 \end{aligned}$$ ∴ Volume of prism = Area of base × height $$\begin{aligned} & =(3 a \times 2 a \times 12) \mathrm{cu} . \mathrm{cm} . \\ & =72 a^{2}=(72 \times 2 \times 2) \mathrm{cu} . \mathrm{cm} . \\ & =288 \mathrm{cu} . \mathrm{cm} . \end{aligned}$$