A cone and a hemisphere have equal bases and equal volume. Find the ratio of their heights.
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Volume and Surface Area of Solids question types
44 questions across 4 question groups — pick any mix to generate a Mathematics paper with step-by-step answer keys.
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Sample Questions
Volume and Surface Area of Solids questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
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An iron sphere of radius 5 cm has been melted and recast into smaller spheres each of radius 2.5 cm. How many smaller spheres are made?
How long would it take to fill a conical vessel whose diameter of base is 20 cm and depth is 21 cm, if it is filling through a pipe of diameter 5 mm, at the rate of 10 m/minute.
How many metres of cloth 5 m wide will be required to make a conical tent, the radius of whose base is 7 m and whose height is 24 m ?
If the volumes of two cylinders are in the ratio $128: 75$, then find the ratio of their curved surface areas. It is given that the ratio of their heights is $2: 3$.
View full solution →From a solid cylinder whose height is $2.4 \ cm,$ and diameter $1.4 \ cm,$ a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest $\ cm^{2.}$
View full solution →A small cone is cut off at the top of a cone by a plane parallel to the base. The volume of the small cone is $\frac{1}{8}$ of the volume of the bigger cone. At what height above the base is the section made, it is given that height of the complete cone is 40 cm ?
View full solution →Two solid iron poles are lying one over other. The pole at the lower position has height $220 \ cm$ and base diameter $24 \ cm,$ whereas the pole above it has height of $60 \ cm,$ and base diameter $16 \ cm.$ Calculate the weight of the pole, if $1 \ cm^3$ of iron weighs $10 \ g.$
View full solution →A plumber fits a pipe of internal radius 10 cm from a tap to a cylindrical tank, which is 5 m in radius and 2 m deep. If the water flows through the pipe at the rate of 3 km/hr, in how much time will tank be filled?
The given figure represents a hemisphere surmounted by a conical block of wood. The diameter of their bases is 6 cm each and the slant height of the cone is 5 cm. Calculate:
(a) the height of the cone.
(b) the volume of the solid.
(a) the height of the cone.
(b) the volume of the solid.
The lateral surface area of a cone is $60 \pi \mathrm{~cm}^2$. If the slant height of the cone be 8 cm , then the diameter of its base is :
- A25 cm
- B18 cm
- C12 cm
- D15 cm
The diameter of a cone is 10 cm and vertical height is 12 cm . Then, the area of curved surface area is:
- A$205.15 \mathrm{~cm}^2$
- B$214.16 \mathrm{~cm}^2$
- C$204.28 \mathrm{~cm}^2$
- D$241.20 \mathrm{~cm}^2$
The diameter of a cone is 28 cm and slant height is 10.5 cm . Then, its lateral surface area is:
- A$480 \mathrm{~cm}^2$
- B$490 \mathrm{~cm}^2$
- C$462 \mathrm{~cm}^2$
- D$466 \mathrm{~cm}^2$
The circumference of the base of a cylindrical vessel is 132 cm and its height is 50 cm . How many litres of water can it hold?
- A34.39 litres
- B70.50 litres
- C69.30 litres
- D67.67 litres
The radius of two cylinders are in the ratio of $2: 3$ and their heights are in the ratio of $5: 3$. The ratio of their volumes is :
- A$10: 17$
- B$20: 27$
- C$17: 27$
- D$20: 37$
Assertion (A) : The maximum volume of a cone that can be carved out of a solid hemisphere of radius $r$ is $\frac{1}{3} \pi r^3$.
Reason (R): For a cone of radius $r$ and height $h$, curved surface area $=\pi r \sqrt{r^2+h^2}$.
Reason (R): For a cone of radius $r$ and height $h$, curved surface area $=\pi r \sqrt{r^2+h^2}$.
- AA is true, R is false.
- BA is false, R is true.
- ✓Both A and R are true, and R is the correct reason for A .
- DBoth A and R are true, and R is incorrect reason for A .
Answer: C.
View full solution →Assertion (A) : Total surface area of a hemisphere of radius 2 cm is $4 \pi \mathrm{~cm}^2$.
Reason (R) : Total surface area of a hemisphere of radius $r$ is $3 \pi r^2$.
Reason (R) : Total surface area of a hemisphere of radius $r$ is $3 \pi r^2$.
- AA is true, R is false.
- ✓A is false, R is true.
- CBoth A and R are true, and R is the correct reason for A .
- DBoth A and R are true, and R is incorrect reason for A .
Answer: B.
View full solution →Assertion (A) : Volume of a cylinder of radius 7 cm and height 10 cm is $490 \pi \mathrm{~cm}^3$.
Reason (R): Volume of a cylinder of base radius $r$ and height $h$ is given by $\pi r^2 h$.
Reason (R): Volume of a cylinder of base radius $r$ and height $h$ is given by $\pi r^2 h$.
- AA is true, R is false.
- BA is false, R is true.
- CBoth A and R are true, and R is the correct reason for A .
- ✓Both A and R are true, and R is incorrect reason for A .
Answer: D.
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