Given height of the cone, h = 20 cm Diameter of the cone = 16.8 cm Radius of the cone, r = 16.8/2 = 8.4 cm Volume of water in the vessel = (1/3)r2h = (1/3)×8.42 ×20 = (1/3)×(22/7)×8.4 ×8.4 ×20 =...
A well with inner diameter 6 m is dug 22 m deep. Soil taken out of it has been spread evenly all round it to a width of 5 m to form an embankment. Find the height of the embankment.
Solution; Given inner diameter of the well = 6 m Radius of the well, r = 6/2 = 3 m Depth of the well, H = 22 m Volume of the soil dug out of well = r2H = ×32×22 = 198 m3 Width of the embankment = 5...
The adjoining figure shows a cuboidal block of wood through which a circular cylindrical hole of the biggest size is drilled. Find the volume of the wood left in the block.
Solution: Given diameter of the hole, d = 30 cm radius of the hole, r = d/2 = 30/2 = 15 cm Height of the cylindrical hole, h = 70 cm Volume of the cuboidal block = lbh = 70×30×30 = 63000 cm3 Volume...
A shot-put is a metallic sphere of radius 4.9 cm. If the density of the metal is 7.8 g per cm3, find the mass of the shot-put.
Solution: Given radius of the metallic sphere, r = 4.9 cm Volume of the sphere, V = (4/3)r3 V = (4/3)×(22/7)×4.93 V = 493.005 V = 493 cm3 (approx) Given Density = 7.8 g per cm3 Density = Mass/...
The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to its base. If its volume be 1/27 of the volume of the given cone, at what height above the base is the section cut?
Solution: Given height of the cone, H = 30 cm Let R be the radius of the given cone and r be radius of small cone. Let h be the height of small cone. Volume of the given cone = (1/3)R2H Volume of...
A conical tent is 10 m high and the radius of its base is 24 m. Find : (i) slant height of the tent. (ii) cost of the canvas required to make the tent, if the cost of 1 m2 canvas is Rs 70.
Solution: (i)Given height of the tent, h = 10 m Radius, r = 24 m We know that l2 = h2+r2 l2 = 102+242 l2 = 100+576 l2 = 676 l = √676 l = 26 (ii) Curved surface area = rl = (22/7)×24×26 = 13728/7 m2...
Find the curved surface area of a right circular cone whose slant height is 10 cm and base radius is 7 cm.
Solution: Given slant height of the cone, l = 10 cm Base radius, r = 7 cm Curved surface area of the cone = rl = (22/7)×7×10 = 220 cm2 Hence the curved surface area of the cone is 220...
Area between the circumferences of two concentric circles is . The inner circle has a circumference of cm, Find the radius of the outer circle.
Given that, Area between the circumferences of two concentric circles is $2464c{{m}^{2}}$ Circumference of inner circle $=132$ cm Circumference $=2\pi r$ $132=2\pi r$ $r=132/2\pi $ $r=\left(...
Find the area enclosed between two concentric circles, their radii are cm and cm respectively.
Given that, Radii of two concentric circles are $6$ cm and $13$ cm respectively. ${{r}^{2}}=6cm$ ${{r}^{2}}=13cm$ Area between two concentric circles = Areas of larger circle – area of smaller...
Area of a circle ring enclosed between two concentric circles is . Find out the radii of the two circles, if their difference is .
Assume r be the radius of inner circle, And $(r+1)$ be the radius of outer circle Area of circular ring = Area of outer circle – Area of inner circle $\pi {{\left( r+1 \right)}^{2}}-\pi...
Diameter of a cycle wheel is. How many revolutions will it make in moving km?
Given that, Diameter of a cycle wheel =$4\frac{5}{11}cm=49/11cm$ Circumference of circle $=\pi d$ Circumference of circle $=22/7\times 49/11$ Circumference of circle $=14cm$ $=1.4m$ Distance...
Circumference of a garden roller is . How many revolutions make in moving meters?
Given that, Circumference of a garden roller $=280cm$ Total distance travelled $=490m$ Number of revolutions $=490/2.8=175$ Answer is $=175$
A bucket is ascended by a rope from well which is wound round a wheel having diameter of 35 cm. If the bucket is ascended from well with a uniform speed of m/sec in 2 minutes , calculate the number of full revolutions the wheel makes while raising the bucket.
According to given question, Diameter of wheel, $d=35cm$ Radius of circle = Half of the diameter $r=d/2$ So, Radius of wheel $=35/2=17.5cm$ Circumference of circle $=2\pi r$ $=2\times 22/7\times...
Car wheels make 9 revolutions per second. The diameter of the wheel is , find its speed in km/hr.
Given that, Diameter of the wheel $=42cm$ Radius of the wheel, r $=42/2=21cm$ Number of revolutions made by a car wheel $=9$ revolutions per second Number of revolutions made by a car wheel per hour...
Speed of the car is . If each wheel of the car is in diameter, calculate the number of revolutions made by each wheel per minute.
Given that, Speed of the car $=66km/h=66000m/h$ Diameter of the wheel $=140cm$ Radius of wheel, $r=140/2=70cm$ Circumference of circle $=2\pi r$ $=2\times 22/7\times 70$ $=440cm$ Circumference of...
The diameter of car wheel is . The car wheel makes 10 revolutions per second. Find the speed of the car in km/hour.
Solution: - According to given question, Wheel Diameter $=70cm$ Radius = Half of the diameter of circle $r=d/2$ $r=70/2$ $r=35cm$ Circumference of circle $=2\pi r$ $=2\times 22/7\times 35$ $=220cm$...
The diameter of a wheel is 1. How many revolutions does wheel make when it covers a distance of distance ?
Solutions:- According to given question- Wheel Diameter $=1.4m$ Radius = Half of the diameter of circle $r=d/2$ $r=1.4/2$ $r=0.7m$ Circumference of circle $=2\pi r$ $=2\times 22/7\times 0.7$ $=4.4m$...
The circle whose area is . Find the circumference of the circle.
Area of the circle is $81\pi c{{m}^{2}}$ Area of circle $=\pi {{r}^{2}}$ $81\pi =\pi {{r}^{2}}$ $81\pi /\pi ={{r}^{2}}$ ${{r}^{2}}=81$ $r=\sqrt{81}$ Hence radius is $r=9cm$ Circumference of circle...
The circumference of circular field is . Find the area.
Solution: - According to question, Circumference of circular field $=396m$ Circumference of circle $=2\pi r$ $396=2\pi r$ $396=2\times \left( 22/7 \right)\times r$ $r=396\times \left( 7/22...
Find the area and perimeter of the following from (iii) Angle at the center,, Diameter .
(iii) According to question, Diameter $=42cm$, angle at the center $={{100}^{\circ }}$ Radius = half of the diameter of the circle $r=d/2$ $r=42/2$ $r=21cm$ Area of the sector $=\left( \pi...
Find the area and perimeter of the following from (i) Angle at the center, Radius (ii) Angle at the center, Radius
(i) According to question, Angle at the center $={{60}^{\circ }}$ radius $=4.2cm$, Area of the sector $=\left( \pi {{r}^{2}}\times \frac{\theta }{{{360}^{\circ }}} \right)$ $=\left[ \left(...
Find the area and perimeter from (i) to (iii) semi-circles:(iii) Diameter of semicircle
(iii) According to question, Diameter of semi-circle, $d=5.6cm$ Radius = half of the diameter of semi-circle $r=d/2$ $r=5.6/2$ $r=2.8cm$ Perimeter of semi-circle $=\left( \pi r+2r \right)$ $=\left[...
Find the area and perimeter from (i) to (iii) semi-circles:(i) Radius of semicircle (ii) Diameter of semicircle
(i) According to question, Radius of semi-circle, $r=1.4cm$ Perimeter of semi-circle $=\left( \pi r+2r \right)$ $=\left[ \left( 22/7 \right)\times \left( 1.4 \right)+\left( 2\times 1.4 \right)...
Find the perimeter and area from (iii) Diameter of circle (iv) Diameter of circle
(iii) According to given question, Diameter of circle, $d=77cm$ Radius = half of the diameter of the circle $r=d/2$ $r=77/2$ So, $r=38.5cm$ perimeter of the circle $=2\pi r$ $=2\times...
Find the perimeter and area from (i) Radius of circle (ii) Radius of circle
(i) According to given question, Radius of circle, $r=2.8cm$ Perimeter of the circle $=2\pi r$ $=2\times \frac{22}{7}\times \left( 2.8 \right)$ $=17.6cm$ Area of the circle $=\pi {{r}^{2}}$...