Question

9. The figure below is a model representing a storage container. The model whose total
height is 15 cm is made up of a conical top, a hemispherical bottom and the middle part is
cylindrical. The radius of the base of the cone and that of the hemisphere are each 3 cm. The
height of the cylindrical part is 8cm.
(a) calculate the perpendicular height (H) of the corn.
(b) calculate the slanting height (L) of the corn.
(c) Calculate the external surface area of the model
(d) Calculate the volume of the model
(e) The actual storage container has a total height of 6 meters. The outside of the actual storage container is to be
painted. Calculate the amount of paint required if an area of 20m2 requires 0.75 liters of the paint.​

Answer 1

Answer:

i. 4cm

ii. 5cm

iii. 254.57cm²

iv. 320.57cm³

v. 9.54l

Step-by-step explanation:

total height = 15cm

cylinder height = 8cm

radius = 3cm

i. cone h = 15-(8+3)

= 15-11 = 4cm

ii. h = 4cm , r = 3cm

l² = h² + r²

l² = (4)² + (3)²

l² = 16+9

l = √25 = 5cm

iii. TSA of model = CSA of cone + CSA of cylinder + CSA of hem.

= πrl + 2πrh + 2πr²

= πr(l + 2h + 2r)

= 22/7*3(5 + 16 + 6)

= 66/7*27

= 254.57cm²

iv. volume of model = vol of cone + vol of cylinder + vol of hem

= 1/3πr²h + πr²h + 2/3πr³

= πr²(1/3h + h + 2/3r)

= 22/7*3*3(1/3*4 + 8 + 2/3*3)

= 66/7(4/3 + 24 + 6)

= 66/7*34

= 320.57cm³

v. paint required = 254.57/20*0.75

= 9.54l