find the height of the toy and also the cost of painting the hemispherical part at the rate of 10rs per square. cm
Answers
Given:
Radius of hemisphere = radius of cone = r = 3.5 cm
Volume of total wood = 166 ⅚ = 1001/6 cm³
height of cone = h
Volume of total wood used in making a toy = volume of hemisphere + volume of cone
Therefore,
⇒(⅔) × πr³ + (⅓)π²h
⇒ (⅓)πr²(2r + h)
⇒1001/6 = (⅓) ×( 22/7) × (3.5)² × (h +2×3.5)
⇒1001/6 = (⅓) ×( 22/7) × 3.5 ×3.5 ×( h+7)
⇒1001/6 = (⅓) × 22 × .5 ×3.5 × (h +7)
⇒1001 × 3 = 6 × 22 × .5 ×3.5 × (h+7)
⇒h +7 = 1001 × 3 / (6 × 22 × .5 ×3.5)
⇒h +7 = 1001 × 3 / 132 × 1.75
⇒h +7 = 1001 × 3 × 100 / 132 × 175
⇒h +7 = 91 × 3 × 4 / 12 × 7
⇒h +7 = 91 × 12 / 12×7
⇒h +7 = 13
⇒h + 7 = 13 -7 = 6
Height of a cone(h) = 6
Height of the toy = Height of a cone + Height of a hemisphere
Height of the toy = 6 +3.5 = 9.5 cm
Curved surface area of hemisphere = 2πr²
CSA of hemisphere = 2 ×( 22/7) × 3.5 × 3.5
= 2 × 22 × .5 × 3.5 = 44 × 1.75 = 77 cm²
Rate of painting the hemispherical part of the toy = ₹ 10 per m².
Cost of painting the hemispherical part of the toy = 77 × 10 = ₹ 770 .
Hence, the Height of the toy is 9.5 m & Cost of painting the hemispherical part of the toy is ₹ 770.
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