###### Advertisements

###### Advertisements

A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs 12 per m^{2}, what will be the cost of painting all these cones?

`("Use "π = 3.14" and take "sqrt1.04= 1.02)`

###### Advertisements

#### Solution

Radius (*r*) of cone = 40/2 = 20cm = 0.2m

Height (*h*) of cone = 1 m

Slant height (*l*) of cone`= sqrt(h^2+r^2)`

`=[sqrt((1)^2+(0.2)^2)]m=sqrt1.04m=1.02m`

CSA of each cone = π*rl*

= (3.14 × 0.2 × 1.02) m^{2} = 0.64056 m^{2}

CSA of 50 such cones = (50 × 0.64056) m^{2}

= 32.028 m^{2}

Cost of painting 1 m^{2} area = Rs 12

Cost of painting 32.028 m^{2} area = Rs (32.028 × 12)

= Rs 384.336

= Rs 384.34 (approximately)

Therefore, it will cost Rs 384.34 in painting 50 such hollow cones.

#### APPEARS IN

#### RELATED QUESTIONS

Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.

`["Assume "pi=22/7]`

Curved surface area of a cone is 308 cm^{2} and its slant height is 14 cm. Find

(i) radius of the base and (ii) total surface area of the cone.

`["Assume "pi=22/7]`

Find the curved surface area of a cone, if its slant height is 60 cm and the radius of its base is 21 cm.

Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24m.

There are two cones. The curved surface area of one is twice that of the other. The slant height of the later is twice that of the former. Find the ratio of their radii.

A conical tent is 10 m high and the radius of its base is 24 m. Find the slant height of the tent. If the cost of 1 2 m canvas is Rs. 70, find the cost of the canvas required to make the tent.

Two cones have their heights in the ratio 1 : 3 and the radii of their bases in the ratio 3 : 1. Find the ratio of their volumes.

Find the volume of the largest right circular cone that can be fitted in a cube whose edge is 14 cm.

A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilo litres?

Monica has a piece of Canvas whose area is 551 m2. She uses it to have a conical tent made, with a base radius of 7m. Assuming that all the stitching margins and wastage incurred while cutting, amounts to approximately 1 m2. Find the volume of the tent that can be made with it.

Find the volume of a cone whose slant height is 17 cm and radius of base is 8 cm.

The radius and the height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the radius and height of the cone (Take π = 3.14)

A heap of wheat is in the form of a cone of diameter 16.8 m and height 3.5 m. Find its volume. How much cloth is required to just cover the heap?

A solid cone of height 8 cm and base radius 6 cm is melted and recast into identical cones each of height 2 cm and diameter 1 cm. Find the number of cones formed.

Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm

A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5cm. Find the number of sphere formed.

A buoy is made in the form of hemisphere surmounted by a right cone whose circular base coincides with the plane surface of hemisphere. The radius of the base of the cone is 3.5 metres and its volume is two third of the hemisphere. Calculate the height of the cone and the surface area of the buoy, correct to two places of decimal

From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm

and depth 24 cm is drilled out. Find: the surface area of remaining solid

A cone and hemisphere have the same base and the same height. Find the ratio between their volumes.

Perpendicular height of a cone is 12 cm and its slant height is 13 cm. Find the radius of the base of the cone.

Curved surface area of a cone is 251.2 cm^{2} and radius of its base is 8 cm. Find its slant height and perpendicular height. (π = 3.14)

What will be the cost of making a closed cone of tin sheet having radius of base 6 m and slant height 8 m if the rate of making is Rs.10 per sq.m? `(π = 22/7)`

volume of a cone is 6280 cubic cm and base radius of the cone is 20 cm. Find its perpendicular height. (π = 3.14)

Surface area of a cone is 188.4 sq.cm and its slant height is 10 cm. Find its perpendicular height ( π= 3.14)

Volume of a cone is 1232 cm^{3} and its height is 24 cm. Find the surface area of the cone. `( π = 22/7)`

The curved surface area of a cone is 2200 sq.cm and its slant height is 50 cm. Find the total surface area of cone. `(π = 22/7)`

If the ratio of radius of base and height of a cone is 5:12 and its volume is 314 cubic metre. Find its perpendicular height and slant height. (π = 3.14)

Total surface area of a cone is 616 sq.cm. If the slant height of the cone is three times the radius of its base, find its slant height.

Find the volume of the right circular cone whose height is 12 cm and slant length is 15 cm . (π = 3.14)

Find the height of the cone whose base radius is 5 cm and volume is 75π cm^{3}.

A sphere and a cone have the same radii. If their volumes are also equal, prove that the height of the cone is twice its radius.

The given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm and the other dimensions are as shown. Calculate: the total volume of the solid.

The given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm and the other dimensions are as shown. Calculate: the density of the material if its total weight is 1.7 kg

A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.

The circumference of the base of a 10 m high conical tent is 44 metres. Calculate the length of canvas used in making the tent if the width of the canvas is 2m. (Take π = 22/7)

Water flows at the rate of 10 m per minute through a cylindrical pipe 5 mm of diameter. How much time would it take to fill a conical vessel whose diameter at he surface is 40 cm and depth is 24 cm?

A conical tent is accommodate to 11 persons each person must have 4 sq. metre of the space on the ground and 20 cubic metre of air to breath. Find the height of the cone.

A right-angled triangle PQR where ∠Q = 90° is rotated about QR and PQ. If QR = 16 cm and PR = 20 cm, compare the curved surface areas of the right circular cones so formed by the triangle

The ratio of the radii of two right circular cones of the same height is 1 : 3. Find the ratio of their curved surface area when the height cone is 3 times the radius of the smaller cone.

The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is