parul has a hollow spherical ball of thickness 3.5cms and external diameter 21cms.she cut the into 2 and painted one of the hemisphere completely.if the cost of paint is rs.2.50 per sq.cm .how much did parul spend on painting?
Answers
Answer:
yug class 5F Present mam
Given:
The thickness of hollow spherical ball = 3.5 cms
The external diameter of hemisphere = 21 cms
The cost of painting the hemisphere = 2.50 per sq.cm.
To find:
We have to find the cost of painting of one hemisphere
Solution:
To know the cost of painting of the hemisphere,first we need to find out the TOTAL SURFACE AREA of a HOLLOW HEMISPHERE.
TSA of a hollow hemisphere is given by the formula,
TSA = 2π(r₂²+r₁²)+π(r₂²-r₁²)
r₂= external radius = 21/2 = 10.5 cms.
r₁ = internal radius = internal diameter/2 = (external diameter-2(thickness))/2
= (21-2(3.5))/2
= (21-7)/2
= 14/2
= 7 cms.
Now, TSA = 2π[ (10.5)² + (7)² ] + π[ (10.5)² -(7)² ]
= 2π[110.25 + 49] + π[110.25 - 49]
= 2π(159.25) + π(61.25)
= 1000.5972 + 192.4225
TSA= 1193.0197
Now the cost of painting the hollow hemisphere = 2.50× TSA
= 2.50×1193.0197
= 2982.5492 Rs.
∴The cost of painting the hollow hemisphere = Rs. 2,982.5