Question

A wodden article was made by scooping out a hemisphere of radius 3 cm, from each end of a solid cylinder of height 10 cm and diameter 14 cm, then find the total surface are of the article.​

Answer 1

$\huge\bf{\underline{Question:}}$

A wodden article was made by scooping out a hemisphere of radius 3 cm, from each end of a solid cylinder of height 10 cm and diameter 14 cm, then find the total surface are of the article.

$\huge\bf{\underline{Solution:}}$

The total surface area of the article would be equal to the sum of curved surface area of two hemispheres at the end and curved surface area of cylinder.

Radius of Cylinder = 7cm

Formulas:

Curved surface area of hemisphere = 2π$\sf{r^2}$

Curved surface area of cylinder = 2πrh

Total Surface Area of Article

$= 2\pi \: rh + 2(2 \pi{r}^{2}) \\ = 2 \times \frac{22}{7} \times 7 \times 10 + 2 \times 2 \times \frac{22}{7} \times {(3)}^{2} \\ = \frac{44}{7} (70+18) \\ = \frac{44}{7} \times 88 \\ = \frac{3872}{7} \\ =553.14c{m}^{2} (approx)$

Therefore,the total surface area of the article is 553.14 sq.cms.

Answer 2

SOLUTION:-

Given:

A wooden article was made by scooping out a hemisphere of radius 3cm,from each end of a solid cylinder of height 10cm & dimeter 14cm.

To find:

The total surface area of the article.

Explanation:

CASE 1.

We know that, formula of the curved surface area of cylinder: 2πrh

We have,

• Height of the cylinder,h=10cm
• Diameter of the cylinder,d=14cm
• Radius of the cylinder,r= 14/2=7cm

Therefore,

C.S.A of cylinder= 2πrh

C.S.A of cylinder=[ 2×$\frac{22}{7}$×7×10]cm²

C.S.A of cylinder=[44×10]cm²

C.S.A of cylinder=440cm².

CASE 2.

We know that, formula of the curved surface area of hemisphere: 2πr².

Therefore,

C.S.A of hemisphere= 2πr² square units

C.S.A of hemisphere= [2× $\frac{22}{7}$×3×3]cm²

C.S.A of hemisphere= [$\frac{44}{7}$×9]cm²

C.S.A of hemisphere= [6.29×9]cm²

C.S.A of hemisphere= 56.61cm².

Surface area of 2 hemisphere= (2× 56.61)cm²

Surface area of 2 hemisphere= 113.22cm².

Now,

The total surface area of the article:

C.S.A of cylinder + C.S.A of 2 hemisphere

⇒ 440cm² + 113.22cm²

⇒ 553.22cm².

Thus,

The total area of article is 553.22cm².