Advertisements
Advertisements
Question
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.
Solution
Area of the base = 11 x 4 = 44 m2
and Volume of the cone = 11 x 20 = 220 m3
`1/3` x πR2h = 220 m3
Area of the base = πR2
∴ πR2 = 44
∴ R2 = `44/22 xx 7`
∴ R2 = 14
∴ R = `sqrt14`
By equation (i) and (ii), we get
`1/3 xx 22/7 xx sqrt14 xx sqrt14 xx h = 220`
h = `(220 xx 3)/(22 xx 2)`
h = `30/2` = 15 cm.
APPEARS IN
RELATED QUESTIONS
A conical tent is 10 m high and the radius of its base is 24 m. Find
- slant height of the tent.
- cost of the canvas required to make the tent, if the cost of 1 m2 canvas is ₹ 70.
`["Assume "pi=22/7]`
The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of ₹ 210 per 100 m2.
`["Assume "pi=22/7]`
Find the curved surface area of a cone with base radius 5.25 cm and slant height 10cm.
The curved surface area of a cone is 4070 cm2 and its diameter is 70 cm. What is its slant height? (Use it 𝜋 = 22/7).
The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of Rs. 210 per l00 m2.
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.
Find the volume of a right circular cone with:
radius 3.5 cm, height 12 cm
The radius and height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the slant height and radius of the cone. (Use it 𝜋 = 3.14).
A heap of wheat is in the form of a cone of diameter 9 m and height 3.5 m. Find its volume. How much canvas cloth is required to just cover the heap? (Use 𝜋 = 3.14).
The volume of a right circular cone is 9856 cm3. If the diameter of the base is 28 cm, find:
(i) height of the cone (ii) slant height of the cone (iii) curved surface area of the cone.
The total surface area of a right circular cone of slant height 13 cm is 90π cm2.
Calculate:
- its radius in cm.
- its volume in cm3. [Take π = 3.14].
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,
- the volume of remaining solid,
- the weight of the material drilled out if it weighs 7 gm per cm3.
The cross-section of a railway tunnel is a rectangle 6 m broad and 8 m high surmounted by a semi-circle as shown in the figure. The tunnel is 35 m long. Find the cost of plastering the internal surface of the tunnel (excluding the floor) at the rate of Rs. 2.25 per m2.
In the following diagram a rectangular platform with a semi-circular end on one side is 22 metres long from one end to the other end. If the length of the half circumference is 11 metres, find the cost of constructing the platform, 1.5 metres high at the rate of Rs. 4 per cubic metres.
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 radius of the circular base of the cone , if its volume is 154 cm3 and the perpendicular height is 12 cm
A hollow metallic cylindrical tube has an internal radius of 3.5 cm and height 21 cm. The thickness of the metal tube is 0.5 cm. The tube is melted and cast into a right circular cone of height 7 cm. Find the radius of the cone, correct to one decimal place.
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.
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.
