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प्रश्न
A pen stand made of wood is in the shape of a cuboid with four conical depression and a cubical depression to hold the pens and pins , respectively . The dimension of the cuboid are \[10 cm \times 5 cm \times 4 cm\].
The radius of each of the conical depression is 0.5 cm and the depth is 2.1 cm . The edge of the cubical depression is 3 cm . Find the volume of the wood in the entire stand.
उत्तर
The dimensions of the cuboid = 10 cm × 5 cm × 4 cm
Volume of the total cuboid = 10 cm × 5 cm × 4 cm = 200 cm3
Radius of the conical depressions, r = 0.5 cm
Depth, h = 2.1 cm
Volume of the conical depression =
\[\frac{1}{3} \pi r^2 h = \frac{1}{3}\pi \left( 0 . 5 \right)^2 \left( 2 . 1 \right) = 0 . 5495\]cm3
Edge of cubical depression, a = 3 cm
Volume of the cubical depression = \[a^3 = 3^3 = 27 c m^3\]
Volume of wood used to make the entire stand = Volume of the total cuboid − volume of conical depression − volume of cubical depression
\[= 200 - 4 \times 0 . 5495 - 27\]
\[ = 170 . 802 c m^3 \]
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Assertion (A)
If the volumes of two spheres are in the ratio 27 : 8, then their surface areas are in the ratio 3 : 2.
Reason (R)
Volume of a sphere `=4/3pi"R"^3`
Surface area of a sphere = 4πR2
Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).- Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
- Assertion (A) is true and Reason (R) is false.
- Assertion (A) is false and Reason (R) is true.
