The radius of the circular base of a cylinder is 14 cm and height is 10 cm. Calculate the curved surface area of the cylinder.
Radius of the circular base of the cylinder (r) = 14 cm Height of the cylinder (h) =10 cm Curved surface area of the cylinder 
The circumference of a thin hollow cylindrical pipe is 44 cm and length is 20 m. Find the surface area of the pipe.
Let r be the radius of the cylindrical pipe. Circumference of the pipe Length of the pipe Surface area of the pipe
A cylinder has a diameter 20 cm and height 18 cm. Calculate the total surface area of the cylinder.
Diameter of the cylinder (d) = 2 × Radius = 20 cm ⇒ Radius of the cylinder (r) = 10 cm Height (h) of the cylinder = 18 cm Total surface area of cylinder Page No 245:
Lateral surface area of a cylinder is 1056 sq. cm and radius is 14 cm. Find the height of the cylinder.
Radius of the cylinder (r) = 14 cm Lateral surface area of the cylinder Let h be the height of the cylinder. Then, Thus, the height of the cylinder is 12 cm. Page No 245:
A mansion has twelve cylindrical pillars each having the circumference 50 cm and height 3.5 m. Find the cost of painting the lateral surface of the pillars at Rs 25 per sq. m.
Let r be the radius of each cylindrical pillar. Circumference of each cylindrical pillar Height of each cylindrical pillar (h) Lateral surface area of each cylindrical pillar Cost of painting 1 m2 = Rs 25 Cost of painting the lateral surfaces of 12 such pillars Page No 245:
The diameter of a thin cylindrical vessel opened at one end is 3.5 cm and height is 5 cm. Calculate the surface area of the vessel.
Diameter of the cylindrical vessel = 3.5 cm ⇒ Radius of the vessel (r) = Height of the vessel (h) = 5 cm Surface area of the vessel Page No 245:
A closed cylindrical tank is made up to a sheet of metal. The height of the tank is 1.3 m and radius is 70 cm. How much sq. m of sheet metal was required?
Height of the cylindrical tank (h) Radius of the tank (r) Area of the required sheet metal = Total surface area of the tank Thus, 8.8 sq. m. of sheet metal is required. Page No 245:
A roller having radius 35 cm and length 1 m takes 200 complete revolutions to move once on a play ground. What us the area of the playground?
Radius of the roller (r) = 35 cm Length of the roller (h) = 1 m =100 cm Area of land covered by the roller in 1 revolution = The roller takes 200 complete revolutions to move once on the playground. ∴ Area of the playground Page No 246:
Area of the base of a right circular cylinder is 154 sq. cm and height is 10 cm. Calculate the volume of the cylinder.
Let r be the radius of the cylinder. Area of the circular base Height of the cylinder (h) = 10 cm Volume of the cylinder Page No 246:
Find the volume of the cylinder whose radius is 5 cm and height is 28 cm.
Radius of the cylinder (r) = 5 cm Height of the cylinder (h) = 28 cm Volume of the cylinder Page No 247:
The circumference of the base of a cylinder is 88 cm and height is 10 cm. Calculate the volume of the cylinder.
Let r be the radius of the cylinder. Circumference of the base of the cylinder Height of the cylinder (h) = 10 cm Volume of the cylinder Thus, the volume of the cylinder is 6160 cm3. Page No 247:
Volume of a cylinder is 3080 cc and height is 20 cm. Calculate the radius of the cylinder.
Let r be the radius of the cylinder. Height of the cylinder (h) = 20 cm Volume of the cylinder Thus, the radius of the cylinder is 7 cm. Page No 247:
A cylindrical vessel of height 35 cm contains 11 litres of juice Find the diameter of the vessel (one litre = 1000 cc.)
Let r be the radius of the cylindrical vessel. Height of the vessel (h) = 35 cm Volume of the vessel Diameter = 2r Page No 247:
Volume of a cylinder is 4400 cc and diameter is 20 cm. Find the height of the cylinder.
Let h be the height of the cylinder. Diameter of the cylinder = 20 cm ∴ Radius of the cylinder (r) = 10 cm Volume of the cylinder Thus, the height of the cylinder is 14 cm. Page No 247:
The height of water level in a circular well is 7 m and its diameter is 10 m. Calculate the volume of water stored in the well.
Height of water level in the well Diameter of the well = 10 m ∴ Radius of the well Volume of water in the well Page No 247:
A thin cylindrical thin can hold only one litre of paint. What is the height of the tin if the diameter of the tin is 14 cm? (One litre = 1000 cc)
Let h be the height of the cylindrical tin. Diameter of the tin = 14 cm ∴ Radius of the tin Volume of the tin Thus, the approximate height of the cylindrical tin is 6.49 cm. Page No 251:
Find the curved surface area of a cone whose circumference of the base is 66 cm and slant height is 12 cm.
Let r be the radius of the cone. Slant height of the cone (l) = 12 cm Circumference of the base of the cone Curved surface area of the cone Page No 251:
The curved surface area of a cone is 440 sq. cm and slant height is 10 cm. Find the radius of the cone.
Let r be the radius of the cone. Slant height of the cone (l) = 10 cm Curved surface area of the cone Thus, the radius of the cone is 14 cm. Page No 251:
The diameter of the cone is 14 cm and slant height is 9 cm. Find the total surface area of the cone.
Diameter of the cone = 14 cm ∴ Radius of the cone (r) = 7 cm Slant height of the cone (l) = 9 cm Total surface area of the cone Page No 251:
Find the total surface area of a conical tomb when the slant height is 8 m and diameter is 12 m.
Diameter of the conical tomb = 12 m ∴ Radius of the tomb (r) = 6 m Slant height of the tomb (l) = 8 m Total surface area of the tomb Page No 251:
The slant height and the diameter of a conical tent are 25 m and 14 m respectively. Calculate the cost of the canvas used at Rs 15 per sq. m.
Diameter of the conical tent = 14 m ∴ Radius of the tent (r) = 7 m Slant height of the tent (l) = 25 m Total surface area of the tent Cost of 1 m2 canvas = Rs 15 ∴ Cost of 550 m2 canvas Thus, the cost of the canvas used in the conical tent is Rs 8250. Page No 251:
The curved surface area of a conical tomb is 528 sq. m and radius is 8 m. Find the height of the tomb.
Let l be the slant height of the conical tomb. Radius of the tomb (r) = 8 m Curved surface area of the tomb Approximate height of the conical tomb (h) Page No 251:
The height of the cone is 5.6 cm and diameter of the base is 8.4 cm. Find the area of the curved surface.
Diameter of the cone = 8.4 cm ∴ Radius of the cone (r) = 4.2 cm Height of the cone (h) = 5.6 cm Slant height of the cone (l) Curved surface area of cone Page No 251:
The height of a conical tent is 28 m and the diameter of the base is 42 m. Find the cost of the canvas used at Rs 20/- per sq. m.
Height of the conical tent (h) = 28 m Diameter of the base of the tent = 42 m ∴ Radius of the base of tent (r) = 21 m Slant height of the tent (l) Curved surface area of the tent Cost of 1 m2 canvas = Rs 20 ∴ Cost of 2310 m2 canvas Thus, the cost of the canvas used in the conical tent is Rs 46200. Page No 253:
Area of the base of a cone is 300 sq. cm and height is 15 cm. Find the volume of the cone.
Area of the base, Height, Volume of the cone Page No 253:
Volume of a cone is 550 cm3 and diameter is 10 cm. Find the height of the cone.
Volume of the cone, Diameter, Radius, Height, Page No 253:
The radius of the base is 10 cm and the height is 21 cm. Find the volume of the cone.
Radius, Height, Volume of the cone Page No 253:
The circumference of the brim of a conical cup is 22 cm and height is 6 cm. How much water does it hold?
Circumference, ⇒ Height, Volume of the conical cup Thus, 77 cm3 of water can be held in the cup. Page No 253:
The volume of a cone is 3080 cm3 and height is 15 cm. Find the radius of the cone.
Volume of the cone Height ∴Radius of the cone Page No 253:
The volume and the height of a cone are 2200 cm3 and 21 cm respectively. Find the diameter of the basic.
Volume of the cone Height Diameter Thus, the diameter of the base is 20 cm. Page No 253:
A meter long metal rod (cylindrical is shape) of radius 3.5 cm is melted and recast to form cones of radius 1 cm and height 2.1 cm. Find the number of cones so formed.
Length of the rod Radius of the rod Volume of the rod Radius of the cone Height of the cone Volume of the cone ∴Number of cones formed Page No 253:
A right angled triangle of sides 21 cm, 28 cm and 35 cm is revolved on the side 28 cm. Name the solid formed and find its volume.
The solid formed is a cone, where the radius is 21 cm and the height is 28 cm Volume of the cone Page No 256:
Find the surface area of a sphere whose radius is 21 cm.
Radius = 21 cm ∴Surface area of the sphere Page No 256:
The circumference of a globe is 88 cm. Calculate the surface area of the globe.
Circumference ⇒ ∴Surface area of the globe Page No 256:
Find the total surface area of a hemisphere of radius 14 cm.
Radius = 14 cm ∴Total surface area of the hemisphere Page No 256:
The circumference of a hemispherical dome is 44 m. Calculate the cost of painting at Rs 20 per sq. m.
Circumference of the dome ⇒ ∴ Surface area of the dome The cost of painting 1 m2 of area is given as Rs 20. Cost of painting the dome Page No 256:
The surface area of a sphere is 154 sq. cm. Find the diameter of the sphere.
Surface area of the sphere ⇒ Diameter of the sphere Page No 256:
A solid sphere of radius 10.5 cm is cut into 2 halves. Find the total surface area of both the hemispheres.
Radius of the sphere ∴Total surface area of both hemispheres Page No 259:
Find the volume of the sphere whose radius is 3 cm.
Radius Volume of the sphere Page No 259:
The diameter of a shot put is 9 cm. Calculate the volume of the shot-put.
Diameter ⇒ r = ∴Volume of the shot put Page No 259:
The depth of a hemispherical water tank is 2.1 m at the centre. Find the capacity of the water tank in litres.
Depth of the water tank = Radius Volume of the water tank Thus, the capacity of the water tank is 19404 L. Page No 259:
Twenty one lead marbles of even size are recast to form a big sphere. Find the volume of the sphere when the radius of each marbles is 2 cm.
Radius of each smaller marble Volume of the sphere formed = Volume of 21 marbles Page No 264:
Draw a plan and calculate the area of a level ground using the information given below.
Here, we observe that Page No 265:
Plan out and find the area of the field from the data given from the Surveyor’s field book
Here, we observe that Page No 265:
Sketch a rough plan and calculate the area of the field ABCDEFG from the following
We observe that Page No 265:
Calculation the area of the field shown in the diagram below: [Measurements are in metre]
It can be seen that
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Find the lateral surface area of two pillars of height of the pillar is 2.1 m and radius is 2.1 m
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