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Cylinder, Cone and Sphere — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsCylinder, Cone and Sphere5 Marks
Question

The given figure shows a solid formed of a solid cube of side $40\ cm$ and a solid cylinder of radius $20 \ cm$ and height $50 \ cm$ attached to the cube as shown.
Find the volume and the total surface area of the whole solid $($Take $\pi = 3.14).$
✓

Answer

Edge of a cube $= I = 40 \ cm$
$\therefore$ Volume of a cube $= I^3 = (40)^3 = 64000 \ cm^3$
Radius of a solid cylinder $= r = 20 \ cm$
Height of a solid cylinder $= h = 50 \ cm$
$\therefore$ Volume of cylinder $= \pi r^2h$
$= 3.14 \times 20 \times 20 \times 50$
$= 62800 \ cm^3$
$\therefore$ Volume of whole solid $=$ Volume of cube $+$ Volume of cylinder
$= (64000 + 62800) \ cm^3$
$= 126800 \ cm^3$
Total surface area of the whole solid
$=$ Total surface area of a cube $+$ Curved surface area of a cylinder
$= 6l^2 + 2\pi rh$
$= 6 \times (40)^2 \times 2 \times 3.14 \times 20 \times 50$
$= 9600 + 6280$
$= 15880 \ cm^2$

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