a tent of shape of a right circular cylinder upto a height of 3m and then becomes a right circular - Maths - Surface Areas and Volumes

Question

a tent of shape of a right circular cylinder upto a height of 3m
and then becomes a right circular conewith height of 13 5m above
the ground calculate the cost of painting the inner side of the
text at the rate of RS 2 PER Sq m if radius of the base is 14m

Chetna Khanna · Accepted Answer

Let r m be the radius of cylindrical base of cylinder of height h₁m.

∴ r = 14 m and h₁ = 3 m

Curved surface area of cylinder = 2 πrh₁ m²

$= 2 \times \frac{22}{7} \times 14 \times 3 m^{2} = 264 m^{2}$

The radius of cylindrical base of cylinder is also equal to the radius of right circular cone.

Let h₂ be the height of cone and l be the slant height of cone.

r = 14 m and h₂ = (13.5 - 3) m = 10.5 m

l² = r² + h₂²

l² = (14)² + (10.5)²

$\Rightarrow l = \sqrt{196 + 110.25} = \sqrt{306.25} = 17.5 m$

∴ Curved surface area of the cone = πrl

$= \frac{22}{7} \times 14 \times 17.5 = 770 m^{2}$

∴ Total area of tent which is to be painted

= Curved surface area of cylinder + Curved surface area of cone

= (264 + 770) m²

= 1034 m²

Now, Cost of painting 1 m² of inner side of tent = Rs 2

∴ Cost of painting 1034 m² inner side of tent = Rs 2 × 1034 = Rs 2068

a tent of shape of a right circular cylinder upto a height of 3m and then becomes a right circular conewith height of 13.5m above the ground calculate the cost of painting the inner side of the text at the rate of RS 2 PER Sq m if radius of the base is 14m