Question

Question 2

The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in the given figure. Eight such spheres are used for this purpose and are to be painted silver.

Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black.

Find the cost of paint required if silver paint costs 25 paise per cm2 and black paint costs 5 paise per cm2.

The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in the given figure. Eight such spheres are used for this purpose and are to be painted silver.

Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black.

Find the cost of paint required if silver paint costs 25 paise per cm2 and black paint costs 5 paise per cm2.

Open in App

Solution

Radius (r) of wooden sphere

=(212)cm=10.5 cm

Surface area of the wooden sphere

=4πr2

=[4×227×(10.5)2]cm2=1386 cm2

Radius (r1)of the circular end of cylindrical support =1.5 cm

Height (h) of the cylindrical support = 7 cm

CSA of the cylindrical support

=2πrh

=[2×227×(1.5)×7]cm2=66 cm2

Area of the circular end of cylindrical support

=πr2

=[2×227×(1.5)2]cm2=7.07 cm2

Area to be painted silver

=[8×(1386−7.07)]cm2=(8×1378.93) cm2=11031.44 cm2

Cost fo ther painting with silver colour =₹ (11031.44×0.25)=₹ 2757.86...(i)

Area to be painted black

=(8×66) cm2=528 cm2

Cost for the painting with black colour =₹ (528×0.05)=₹ 26.40...(ii)

Total cost in painting

= ₹ (2757.86 + 26.40) [from (i)and(ii)]

= ₹ 2784.26

Therefore, it will cost ₹ 2784.26 for painting in such a way.

=(212)cm=10.5 cm

Surface area of the wooden sphere

=4πr2

=[4×227×(10.5)2]cm2=1386 cm2

Radius (r1)of the circular end of cylindrical support =1.5 cm

Height (h) of the cylindrical support = 7 cm

CSA of the cylindrical support

=2πrh

=[2×227×(1.5)×7]cm2=66 cm2

Area of the circular end of cylindrical support

=πr2

=[2×227×(1.5)2]cm2=7.07 cm2

Area to be painted silver

=[8×(1386−7.07)]cm2=(8×1378.93) cm2=11031.44 cm2

Cost fo ther painting with silver colour =₹ (11031.44×0.25)=₹ 2757.86...(i)

Area to be painted black

=(8×66) cm2=528 cm2

Cost for the painting with black colour =₹ (528×0.05)=₹ 26.40...(ii)

Total cost in painting

= ₹ (2757.86 + 26.40) [from (i)and(ii)]

= ₹ 2784.26

Therefore, it will cost ₹ 2784.26 for painting in such a way.

1

View More

Join BYJU'S Learning Program

Join BYJU'S Learning Program