# A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is $10cm$ ,and its base is of radius $3.5cm$ , find the total surface area of the article.

Last updated date: 19th Mar 2023

•

Total views: 308.1k

•

Views today: 8.87k

Answer

Verified

308.1k+ views

Hint: According to the diagram the wooden article is made of a solid cylinder with a hemi-spherical cavity on both ends. so for solving this problem we use the formulas of curved surface area of cylinder and hemisphere.

Given the radius of base of cylinder is $r = 3.5cm$

And height of the cylinder is $h = 10cm$

From the figure above, it is clear that the total surface area of the wooden article is given by

TSA $ = $ Curved surface area of the cylinder$ + 2 \times $ Curved surface area of hemisphere

Curved surface area of cylinder

$

= 2\pi rh = 2 \times 3.1415 \times 3.5 \times 10 \\

= 219.911c{m^2} \\

$

We know that curved surface area of a sphere $ = 4\pi {r^2}$

Therefore, curved surface area of hemisphere

\[ = \dfrac{1}{2} \times \] Curved surface area of a sphere.

\[ = \dfrac{1}{2} \times 4\pi {r^2} = 2\pi {r^2} = 2 \times 3.1415 \times 3.5 \times 3.5 = 76.96c{m^2}\]

Therefore, TSA $ = 219.911 + 2 \times 76.96 = 373.84c{m^2}$

Hence the Total Surface area of the article is $373.84c{m^2} \cong 374c{m^2}$.

Note: In these types of questions always remember the formula of curved surface area of the geometrical solids involved. Also try to visualise the sold in order to get a better understanding of the area asked in the problem. Always specify the units along with the answer.

Given the radius of base of cylinder is $r = 3.5cm$

And height of the cylinder is $h = 10cm$

From the figure above, it is clear that the total surface area of the wooden article is given by

TSA $ = $ Curved surface area of the cylinder$ + 2 \times $ Curved surface area of hemisphere

Curved surface area of cylinder

$

= 2\pi rh = 2 \times 3.1415 \times 3.5 \times 10 \\

= 219.911c{m^2} \\

$

We know that curved surface area of a sphere $ = 4\pi {r^2}$

Therefore, curved surface area of hemisphere

\[ = \dfrac{1}{2} \times \] Curved surface area of a sphere.

\[ = \dfrac{1}{2} \times 4\pi {r^2} = 2\pi {r^2} = 2 \times 3.1415 \times 3.5 \times 3.5 = 76.96c{m^2}\]

Therefore, TSA $ = 219.911 + 2 \times 76.96 = 373.84c{m^2}$

Hence the Total Surface area of the article is $373.84c{m^2} \cong 374c{m^2}$.

Note: In these types of questions always remember the formula of curved surface area of the geometrical solids involved. Also try to visualise the sold in order to get a better understanding of the area asked in the problem. Always specify the units along with the answer.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE