Question

A cubical block of side 10 cm is surmounted by a hemisphere. What is
the largest diameter that the hemisphere can have ? Find the cost of
painting the total surface area of the solid so formed, at the rate of ? 6
per 100 sq. cm. [Use pi = 3.14]​

Answer 1

Step-by-step explanation:

The total surface area of the solid =Total surface area of the cube+Curved surface area of the hemisphere−Area of the base of the hemisphere.

=6a

2

+2πr

2

−πr

2

=[6×10

2

+2×3.14×5

2

−3.14×5

2

]cm

2

=600+157−78.5=678.5cm

2

Cost of painting=Rs.5 per 100cm

2

∴,Cost of painting the solid=678.5×

100

5

=Rs.33.90

Answer 2

Answer:

$\huge\mathcal{\green{Hola!}}$

$\huge\mathfrak{\red{Answer}}$

$\huge\rightarrow\bf d = 10cm$

$\huge\rightarrow\bf ₹ \ 40.71$

Step-by-step explanation:

$\huge\underline{\overline{\mid{\bold{\blue{\mathcal{ \ Question:-}}\mid}}}}$

A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have ? Find the cost of painting the total surface area of the solid so formed, at the rate of ₹6 per 100 square cm.

$\huge\underline{\overline{\mid{\bold{\blue{\mathcal{ \ Hint:-}}\mid}}}}$

For this question;

• Firstly we will find the surface area of the cubical block and the curved surface area of the hemisphere, it will give the total Surface area of the solid.
• Then we will multiply the rate of painting per sq. cm with the total Surface area to get our required solution.

$\huge\underline{\overline{\mid{\bold{\blue{\mathcal{ \ Required \ Solution:-}}\mid}}}}$

Side of the square given = 10cm

• Hence, the largest possible diameter is 10cm.

$\fbox{\purple{Greatest \ diameter \ ↝ \ 10cm}}$

$\mathcal{\green{Now,}}$

Radius of the hemisphere, r = 10/2 cm = 5cm.

• We need to paint the solid. So, we need to paint the whole cube and the curved surface area of the hemisphere except its base.

$\mathcal{\green{Now,}}$

• Total Surface area of cube = 6(a)^2 = 6 × 100 = 600cm^2

$\mathcal{\green{And}}$

• The curved surface area of the hemisphere = 2πr^2 = 2× 314/100 ×25 => 157cm^2

• Area of the base of hemisphere = πr^2 = 314/100× 25

=> 78.5cm^2

$\mathcal{\green{Now,}}$

Total Surface area to be painted = surface area of the cube + curved surface area of the hemisphere - area of the base of hemisphere

$= 600 {cm}^{2} + 157 {cm}^{2} - 78.5 {cm}^{2}$

$= 600 {cm}^{2} + 78.5 {cm}^{2} = 678.5 {cm}^{2}$

We know that

• Cost of painting per 100 sq. cm is ₹ 6
• Hence, cost of painting per sq. cm is ₹ 0.06

Required cost is:

$678.5 \times 0.06 = ₹40.71$

$\fbox{\purple{↝ ₹ \ 40.71}}$

_________________________________________________

$\huge\mathcal{\green{All \ the \ very \ best!}}$

$\small\mathfrak{\red{@MissTranquil}}$

$\huge\fbox{\orange{be \ brainly}}$