Two vertices of $\triangle \mathrm{ABC}$ are $\mathrm{A}(1,-6)$ and $\mathrm{B}(-5,2)$. Let the third vertex be $\mathrm{C}(\mathrm{a}, \mathrm{b})$. => the coordinates of its centroid are...
A toy is in the form of a cone of radius $3.5cm$ mounted on a hemisphere of same radius. The total height of the toy is $15.5cm$. Find the total surface area of the toy.
According to the question, Radius of the conical portion of the toy $=3.5cm=r$ Total height of the toy $=15.5cm=H$ If H is the length of the conical portion Now, Length of the cone (h)...
A vessel in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is $14cm$ and the total height of the vessel is $13cm$. Find the inner surface area of the vessel.
As per the question it is given that, Diameter of the hemisphere $=14cm$ Thus, the radius of the hemisphere $=7cm$ Total height of the vessel $=13cm=h+r$ Thus, Inner surface area of the vessel...
A cylindrical road roller made of iron is $1m$ long. Its internal diameter is $54cm$ and the thickness of the iron sheet used in making roller is $9cm$. Find the mass of the road roller, if $1c{{m}^{3}}$ of the iron has $7.8gm$ mass.
As per the question it is given that, Height/length of the cylindrical road roller $=h=1m=100cm$ Internal Diameter of the cylindrical road roller $=54cm$ Thus, the internal radius of the cylindrical...
A cylindrical vessel of diameter $14cm$ and height $42cm$ is fixed symmetrically inside a similar vessel of diameter 16cm and height of $42cm$. The total space between the two vessels is filled with cork dust for heat insulation purposes. How many cubic cms of the cork dust will be required?
According to the question it is given that, Depth of the cylindrical vessel = Height of the cylindrical vessel $=h=42cm$ (common for both) Inner diameter of the cylindrical vessel $=14cm$ Thus, the...
A solid is composed of a cylinder with hemispherical ends. If the complete length of the solid is $104cm$ and the radius of each of the hemispherical ends is $7cm$, find the cost of polishing its surface at the rate of $Rs.10$ per $d{{m}^{2}}$.
According to the question it is given that, Radius of the hemispherical end (r) $=7cm$ Height of the solid $=(h+2r)=104cm$ $\Rightarrow h+2r=104$ $\Rightarrow h=104-\left( 2\times 7 \right)$ Then,...
A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is $14/3$ and the diameter of the hemisphere is $3.5m$. Calculate the volume and the internal surface area of the solid.
As per the question it is given that, Diameter of the hemisphere $=3.5m$ Thus, the radius of the hemisphere (r) $=1.75m$ Height of the cylinder (h) $=14/3m$ We all know that, volume of the Cylinder...
A boiler which is in the form of a cylinder $2m$ long with hemispherical ends each of $2m$ diameter. Find the volume of the boiler.
According to the question, Diameter of the hemisphere $=2m$ So, the radius of the hemisphere (r) $=1m$ Height of the cylinder $\left( {{h}_{1}} \right)=2m$ Then, the volume of the Cylinder $=\pi...
A tent is in the form of a cylinder of diameter $20m$ and height $2.5m$, surmounted by a cone of equal base and height $7.5m$. Find the capacity of tent and the cost of the canvas at $Rs100$ per square meter.
As per the question, Diameter of the cylinder $=20m$ Thus, its radius of the cylinder (R) $=10m$ Height of the cylinder $\left( {{h}_{1}} \right)=2.5m$ Radius of the cone $=$ Radius of the cylinder...
A conical hole is drilled in a circular cylinder of height $12cm$ and base radius $5cm$. The height and base radius of the cone are also the same. Find the whole surface and volume of the remaining Cylinder.
As per the question it is given that, Height of the circular Cylinder $\left( {{h}_{1}} \right)=12cm$ Base radius of the circular Cylinder (r) $=5cm$ Height of the conical hole $=$ Height of the...
A petrol tank is a cylinder of base diameter $21cm$ and length $18cm$ fitted with the conical ends each of axis length $9cm$. Determine the capacity of the tank.
It is given that, Base diameter of the cylindrical base of the petrol tank $=21cm$ Thus, its radius (r) $=diameter/2=21/2=10.5cm$ Height of the Cylindrical portion of the tank $\left( {{h}_{1}}...
A circus tent has a cylindrical shape surmounted by a conical roof. The radius of the cylindrical base is $20cm$. The heights of the cylindrical and conical portions is $4.2cm$ and $2.1cm$ respectively. Find the volume of that tent.
As per the question it is given, Radius of the cylindrical portion (R) $=20m$ Height of the cylindrical portion $\left( {{h}_{1}} \right)=4.2m$ Height of the conical portion $\left( {{h}_{2}}...
Consider a cylindrical tub having radius as $5cm$ and its length $9.8cm$. It is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed in tub. If the radius of the hemisphere is $3.5cm$ and the height of the cone outside the hemisphere is $5cm$, find the volume of water left in the tub.
According to the question we have, The radius of the Cylindrical tub (r) $=5cm$ Height of the Cylindrical tub (H) $=9.8cm$ Height of the cone outside the hemisphere (h) $=5cm$ Radius of the...
A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical parts are $5cm$ and $13cm$, respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Find the surface area of the toy if the total height of the toy is $30cm$.
It is given in the question that, Height of the Cylindrical portion (H) $=13cm$ Radius of the Cylindrical portion (r) $=5cm$ Height of the whole solid $=30cm$ Now, The curved surface area of the...
A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is $3.5cm$ and the height of the cylindrical and conical portions are $10cm$ and $6cm$, respectively. Find the total surface area of the solid. (Use $\pi =22/7$).
According to the question, Radius of the common base (r) $=3.5cm$ Height of the cylindrical part (h) $=10cm$ Height of the conical part (H) $=6cm$ Assume, ‘l’ be the slant height of the cone Now, we...
A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of the cone are $6cm$ and $4cm$, respectively. Determine the surface area of the toy.
It is given in the question that, The height of the cone (h) $=4cm$ Diameter of the cone (d) $=6cm$ Then, its radius (r) $=3$ Assume, ‘l’ be the slant height of cone. Now, we all know that...
A tent of height $77dm$ is in the form of a right circular cylinder of diameter $36m$ and height $44dm$ surmounted by a right circular cone. Find the cost of the canvas at $Rs.3.50$ per ${{m}^{2}}$
According to the question, Height of the tent $=77dm$ Height of a surmounted cone $=44dm$ Height of the Cylindrical Portion $=$ Height of the tent $–$ Height of the surmounted Cone $=77–44$...
A rocket is in the form of a circular cylinder closed at the lower end with a cone of the same radius attached to the top. The cylinder is of radius $2.5m$ and height $21m$ and the cone has the slant height $8m$. Calculate the total surface area and the volume of the rocket.
According to the question it is given that, Radius of the cylindrical portion of the rocket (R) $=2.5m$ Height of the cylindrical portion of the rocket (H) $=21m$ Slant Height of the Conical surface...
A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is $24m$. The height of the cylindrical portion is $11m$ while the vertex of the cone is $16m$ above the ground. Find the area of canvas required for the tent.
As per the question, The diameter of the cylinder (also the same for cone) $=24m$. Thus, its radius (R) $=24/2=12m$ The height of the cylindrical part $\left( {{H}_{1}} \right)=11m$ Now, Height of...