Question : The length, breadth, and height of a wooden box with a lid are 10 cm, 9 cm, and 7 cm, respectively. The total inner surface of the closed box is 262 cm2. The thickness of the wood (in cm) is:
Option 1: $2$
Option 2: $3$
Option 3: $\frac{23}{3}$
Option 4: $1$
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Correct Answer: $1$
Solution : Given: Inner surface area = 262 cm 2 The length, breadth, and height are 10 cm, 9 cm, and 7 cm, respectively. Let the thickness of the wood be $x$ cm. Surface area of the cuboid = 2(length × breadth + length × height + breadth × height) Area of inner surface $= 2(9 - 2x)(10 - 2x) + 2(9 -2x)(7 - 2x) + 2(10- 2x)(7 - 2x)$ $⇒ 262 = 2(9 - 2x)(10 - 2x) + 2(9 -2x)(7 - 2x) + 2(10 - 2x)(7- 2x)$ Putting the value of $x = 1,$ the above equation is satisfied. Hence, the correct answer is $1$.
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Question : The external diameter of an iron pipe is 20 cm and its length is 12 cm. If the thickness of the pipe is 1 cm, find the surface area of the pipe (take $\pi=\frac{22}{7}$ ) correct to two places of decimal.
Question : The curved surface area and the volume of a cylindrical object are 88 cm2 and 132 cm3, respectively. The height (in cm) of the cylindrical object is: (Take $\pi=\frac{22}{7}$ )
Question : If the side of a cubical box is 12 cm, then find its total surface area.
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