Question

Q.10 The area of the whole surface of a cone is 64 sq. m. and the slant height is 5 times the
radius of the base. Find the radius of the base.​

Answer 1

Step-by-step explanation:

Surface area of cone is given by πrs

where s is slant height.

According to question, if radius is x then s must be 5x

So (π)(x)(5x) = 64sq.m

π5x^2 = 64sq.m

Taking pie = 22/7

x= √(64×7/5×22)

= √4.07

= 2.017m

So x = 2.017m

Answer 2

Answer:

We can find the radius of the base using the area of the whole surface of a cone is 64 sq. m. and the slant height is 5 times the radius of the base.

Final Answer: Radius of the base r = $1.84m$

Step-by-step explanation:

From the given question,

• The area of the whole surface of a cone $=64m^2$

•                                   Radius of the base  $=r$

•                                               Slant height  $=l$

• The area of the whole surface of a cone  $=\pi r(r+l)$

Step 1:

• Equate the formula of area of a cone and area value.That is,

                   $\pi r(r+l)=64$

Step 2:

• slant height is 5 times the radius of the base.That is,

         Slant height  $l=5\times r$

• Substitute $l$ value in step 1.

                $\pi r(r+5r)=64$

                      $\pi r(6r)=64$

                         $6\pi r^2=64$

Step 3:

• The value of $\pi$ is $3.14$.
• Substitute $\pi$ value in step 2 equation.

            $6\times 3.14\times r^2=64$

                             $r^2=\frac{64}{6\times 3.14}$

                             $r^2=\frac{64}{18.84}$

                             $r^2=3.397$

Step 4:

• To find the radius value $r$ take square root for step 3 equation.

                              $r=\sqrt{3.397}$

                              $r=1.84m$

Final Answer:

Radius of the base r = $1.84m$