Mathematics
The given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm, and the other dimensions are as shown.
Calculate :
(i) the total surface area,
(ii) the total volume of the solid and
(iii) the density of the material if its total weight is 1.7 kg.
Mensuration
ICSE
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Answer
(i) Given,
Diameter of cone, cylinder and hemisphere = 10 cm
Radius of cone, cylinder and hemisphere (r) = = 5 cm.
From figure,
Height of cone (h) = 12 cm
By formula,
⇒ l2 = r2 + h2
⇒ l2 = 52 + 122
⇒ l2 = 25 + 144
⇒ l2 = 169
⇒ l = = 13 cm.
Total surface area = Surface area of cone + Surface area of cylinder + Surface area of hemisphere
= πrl + 2πrh + 2πr2
= πr(l + 2h + 2r)
=
=
=
= 738.57 cm2.
Hence, surface area of figure = 738.57 cm2.
(ii) From figure,
Volume of figure = Volume of cone + Volume of cylinder + Volume of hemisphere
Hence, volume of figure = 1519.05 cm3.
(iii) By formula,
Density =
Given,
Mass = 1.7 kg = 1700 gm
Substituting values we get,
Density = = 1.12 g/cm3.
Hence, density of material = 1.12 g/cm3.
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