The ratio of two cones volume is $4: 5$ ratio of their radius is $2: 3$. So, ratio of their height is _______ $(9: 1,9: 5: 9)$
View full solution →Question types
Surface Areas and Volumes question types
42 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
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19 Q→054 Marks Questions
5 Q→Sample Questions
Surface Areas and Volumes questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If the radius of a cone is $7\ cm$ and slant height is $25\ cm$ then its height is _______ $cm .(24,12,25)$
View full solution →Total surface area is _______ of the given figure. $\left(6 \pi r^2, 8 \pi r^2, 7 \pi^2\right)$
View full solution →Volume of cube is $27 cm ^3$, then Total surface area is _______ $ cm ^2 .(64,54,27)$
View full solution →Ratio of two spheres surface area is $1: 2$ then ratio of their volume is _______ $\cdot(1: 2,1: \sqrt{2}, 1: 2 \sqrt{2})$
View full solution →Which two figures are included in Mason's square? (Black smith is used to check if wall is straight or not)
If the radius is increase $20 \%$ of the sphere then how much percent its volume increased ?
View full solution →Write total surface area of the close hemisphere.
Write equation of total surface area of cuboid.
If radii of one cylinder and a one cone is equal their heights are also equal then find the ratio of volume of cylinder and volume of cone.
A spherical glass vessel has a cylindrical neck $8\ cm$ long, $2\ cm$ in diameter the diameter of the spherical part is $8.5\ cm$. By measuring the amount of water it holds, a child finds its volume to be $345\ cm^3$. Check whether she is correct, taking the above as the inside measurements and $\pi $ $= 3.14$.
View full solution →A solid iron pole consists of a cylinder of height $220$ cm and base diameter $24$ cm is surmounted by another cylinder of height $60\ cm$ and radius $8\ cm$. Find the mass of the pole, given that $1\ cm^3$ of iron has approximately $8$ g mass. $($Use $\pi = 3.14)$
View full solution →A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are $15\ cm$ by $10\ cm$ by $3.5\ cm$. The radius of each of the depressions is $0.5\ cm$ and the depth is $1.4\ cm$. Find the volume of wood in the entire stand.
View full solution →A wooden article was made by scooping out a hemisphere from each end of a solid cylinder as shown in figure. If the height of the cylinder is $10\ cm$ and its base is of radius $3.5\ cm$, Find the total surface area of the article.
View full solution →Mayank made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end (see Fig.). The height of the cylinder is $1.45\ m$ and its radius is $30\ cm$. Find the total surface area of the bird-bath.
(Take $\pi = \frac{22}{7}$ )
View full solution →(Take $\pi = \frac{22}{7}$ )
A solid is consisting of a right circular cone of height $120 \ cm$ and radius $60 \ cm$ standing on a hemisphere of radius $60 \ cm$. It is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is $60 \ cm$ and its height is 180 cm.
View full solution →A vessel is in the form of an inverted cone. Its height is $8 \ cm$ and the radius of its top, which is open, is $5 \ cm$. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius $0.5 \ cm$ are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
View full solution →A gulab jamun, contains sugar syrup up to about $30\%$ of its volume. Find approximately how much syrup would be found in $45$ gulab jamun, each shaped like a cylinder with two hemispherical ends with length $5 \ cm$ and diameter $2.8 \ cm.$
View full solution →Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is $3 \ cm$ and its length is $12 \ cm$. If each cone has a height of $2 \ cm$, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same).
View full solution →A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to $1 \ cm$ and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.
View full solution →A solid is consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm. It is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is $2 \ cm$ and the diameter of the base is $4 \ cm.$ Determine the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference of the volume of the cylinder and toy. $($Take $\pi = 3.14)$
View full solution →A wooden toy rocket is in the shape of a cone mounted on a cylinder as shown in given below figure. The height of the entire rocket is $26 \ cm,$ while the height of the conical part is $6 \ cm.$ The base of the conical portion has a diameter of $5 \ cm,$ while the base diameter of the cylindrical portion is $3 \ cm.$ If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. $($Take $\pi =3.14)$
View full solution →A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of ₹ 500 per m2. (Note that the base of the tent will not be covered with canvas.)
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