Question

A cylindrical iron pillar 42cm high and 6cm in radius is surmounted by a cone of same radius. If the height of the cone is 7cm, find-
i) the weight of the iron pillar if 1 cubic centimeter of iron weighs 4.5 grams.
ii) the cost of painting the outer cylindrical wall of the pillar at the rate of Rs. 10 per cm2.​

Answer 1

Answer:

गाँव के कौन लोग किस किस काम में जुड गएगाँव के कौन लोग किस किस काम में जुड गएगाँव के कौन लोग किस किस काम में जुड गएगाँव के कौन लोग किस किस काम में जुड गएगाँव के कौन लोग किस किस काम में जुड गएगाँव के कौन लोग किस किस काम में जुड गएगाँव के कौन लोग किस किस काम में जुड गए

Step-by-step explanation:

Answer 2

Given:

Height of cylinder = 42 cm

Radius of cylinder = 6cm

Radius of surmounted cone = 6cm

Height of surmounted cone = 7cm

Weight of 1cm³ of iron = 4.5 grams

Cost of painting wall per cm² = Rs 10

To find:

Weight of iron pillar.

Total cost of painting the wall.

Solution:

Let height and radius of cylinder be $H$ and $R$ respectively.

Let height and radius of surmounted cone be $h$ and $r$ respectively.

Here, $R=r$.

Volume of cone = $\frac{1}{3 } \pi r^{2}h$

Volume of cylinder = $\pi R^{2}H$

Let $V$ be the volume of iron pillar.

Total volume of the iron pillar = Volume of cylinder + Volume of cone

Volume of iron pillar, $V=\pi R^{2}H+\frac{1}{3}\pi r^{2}h$

$V=\pi r^{2}(H+\frac{1}{3}h)$

$V=\frac{22}{7}*6^{2} (42+\frac{7}{3})$

$V=\frac{22}{7}*6^{2}*\frac{133}{3}$

$V=5016cm^{3}$

Hence, volume of the iron pillar is $5016cm^{3}$.

i) $1cm^{3}$ of iron weighs 4.5 grams, so the weight of $5016cm^{3}$ of iron can be determined by multiplying $4.5$ with $5016$.

Weight of $5016cm^{3}$ of iron = $4.5*5016=22572grams$

$1kg=1000g$

$22572g=22.572kg$

Thus, weight of $5016cm^{3}$ of iron is $22572 g$.

ii) To find the area to be painted on the outer cylindrical wall, we must first find the curved surface area of the cylinder. Let this area be $A$.

Curved surface area of a cylinder, $A=2\pi RH$

$A=2\pi *42*6$

$A=2*\frac{22}{7}*42*6$

$A=1584cm^{2}$

To determine the total cost of painting the outer cylindrical wall at Rs 10/cm², multiply the area obtained with 10.

Total cost of painting the wall = Rate/cm² × Area of wall

Total cost of painting the wall = $10*1584=Rs15840$

Hence, Rs 15840 is required to paint the outer cylindrical wall at Rs 10/cm².

Weight of the iron pillar with a cylindrical part surmounted by a conical part is 22572g and the total cost of painting the cylindrical outer wall is Rs 15840.