Question

the perpendicular height of a. cone is 35cm and its volume is2970cu.cm find the diameter of the base​

Answer 1

Answer:

Let r and l be the radius and the slant height of the solid right circular cone respectively.

r=35cm,l=37cm

Curved Surface area, CSA=πrl=π(35)(37)

CSA=4070sq.cm

Total surface area, TSA=πr(l+r)

=

7

22

×35×(37+35)

Thus, TSA=7920sq.cm

Answer 2

S O L U T I O N :

$\underline{\bf{Given\::}}$

• Height of a cone, (h) = 35 cm
• Volume of cone, (V) = 2970 cm³

$\underline{\bf{Explanation\::}}$

As we know that formula of the volume of cube;

$\boxed{\bf{Volume= \frac{1}{3} \pi r^{2}h\:\:(cubic\:unit)}}$

A/q

$\mapsto\tt{2970 = \dfrac{1}{3} \times \dfrac{22}{\cancel{7}} \times r^{2} \times \cancel{35}}$

$\mapsto\tt{2970 = \dfrac{1}{3} \times 22 \times r^{2}\times 5}$

$\mapsto\tt{2970 \times 3 =110\times r^{2}}$

$\mapsto\tt{8910 = 110\times r^{2}}$

$\mapsto\tt{r^{2} = \cancel{\dfrac{8910}{110} }}$

$\mapsto\tt{r^{2} = 81}$

$\mapsto\tt{r = \sqrt{81} }$

$\mapsto\bf{r= 9\:cm}$

So, radius of the cone is 9 cm.

As we know that diameter of cone;

→ Diameter of cone = 2 × radius

→ Diameter of cone = 2 × 9 cm

→ Diameter of cone = 18 cm .