Answer

Verified

429.6k+ views

**Hint:**Here we will use the formula of CSA (Curved surface area) of the cylinder for calculating the radius of the cylinder which equals to as below:

\[{\text{Curved surface area}} = 2\pi rh\]

Where \[r\] is known as the radius of the base of the cylinder, \[h\] is the height of the cylinder.

**Complete step-by-step solution:**

Step 1: From the below diagram we can see that the height of the cylinder is given which is \[14{\text{ cm}}\] and \[r\] is the radius of the base of the cylinder.

\[{\text{Curved surface area}} = 88{\text{ c}}{{\text{m}}^2}\]

Step 2: Now, by using the formula of the curved surface area of the cylinder and by substituting the values of \[h = 14{\text{ cm}}\]and \[\pi = \dfrac{{22}}{7}\] , and \[{\text{Curved surface area}} = 88{\text{ c}}{{\text{m}}^2}\], we get:

\[88{\text{ c}}{{\text{m}}^2} = 2 \times \dfrac{{22}}{7} \times r \times 14{\text{ cm}}\] ……………. (1)

By dividing \[14\] with \[7\] into the RHS side of the expression (1), we get:

\[ \Rightarrow 88{\text{ c}}{{\text{m}}^2} = 2 \times 22 \times r \times 2{\text{ cm}}\]

By bringing all the terms of the RHS side into the LHS side in the expression \[88 = 2 \times 22 \times r \times 2\] , we get:

\[ \Rightarrow \dfrac{{88{\text{ c}}{{\text{m}}^2}}}{{2 \times 22 \times 2{\text{ cm}}}} = r\]

By dividing into the LHS side we get:

\[ \Rightarrow 1{\text{ cm}} = r\]

**\[\therefore \] The radius of the base of the cylinder is equal to \[1{\text{ cm}}\]**

**Note:**Students need to remember some basic formulas for finding surface areas of the cylinder because there are two types of area, one is a Curved surface area and the second is the Total surface area. The formulas for finding both is given below:

\[{\text{Curved surface area}} = 2\pi rh\]

The total surface area of the cylinder\[ = 2\pi r\left( {r + h} \right)\], where \[r\] is known as the radius of the base of the cylinder, \[h\] is the height of the cylinder.

Similarly, the formula for finding the volume of the cylinder is as below:

\[{\text{Volume of the cylinder}} = \pi {r^2}h\]

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

How do you graph the function fx 4x class 9 maths CBSE

Difference Between Plant Cell and Animal Cell

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

What organs are located on the left side of your body class 11 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE