The number of solid spheres, each of diameter $6 \ cm$ that can be made by melting a solid metal cylinder of height $45 \ cm$ and diameter $4 \ cm$ , is:
- A$3$
- ✓$5$
- C$4$
- D$6$
Answer: B.
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Surface Areas and Volumes question types
98 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
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M.C.Q (1 Marks)
35 Q→021 Marks Question
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29 Q→055 Marks Questions
23 Q→06Case study (4 Marks)
2 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.
A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base. The ratio of the volume of the smaller cone to the whole cone is
- A$1: 2$
- B$1: 4$
- C$1: 6$
- ✓$1: 8$
Answer: D.
View full solution →A sphere of diameter $18 \ cm$ is dropped into a cylindrical vessel of diameter $36 \ cm ,$ partly filled with water. If the sphere is completely submerged, then the water level rises $($in $\ cm )$ by
- ✓$3$
- B$4$
- C$5$
- D$6$
Answer: A.
View full solution →The volume of a right circular cone whose area of the base is $156 cm^2$ and the vertical height is 8 cm , is
- A$2496 cm^3$
- B$1248 cm^3$
- C$1664 cm^3$
- ✓$416 cm^3$
Answer: D.
View full solution →The total surface area of a frustum$-$shaper glass tumbler is $\left( r _1 > r _2\right)$
- A$\pi r _1 l+\pi r _2 l$
- ✓$\pi l\left(r_1+r_2\right)+\pi r_2^2$
- C$\frac{1}{3} \pi h\left(r_1^2+r_2^2+r_1 r_2\right)$
- D$\sqrt{h^2+\left(r_1-r_2\right)^2}$
Answer: B.
View full solution →Volume and surface area of a solid hemisphere are numerically equal.
What is the diameter of hemisphere?
What is the diameter of hemisphere?
If the radii of two spheres are in the ratio $2: 3$, then the ratio of their respective volumes is $.......$
View full solution →If the total surface area of a solid hemisphere is $462 \ cm^2$, find its volume. $[$Take $\pi=\frac{22}{7}]$
View full solution →A solid sphere of radius $10.5 \ cm$ is melted and recast into smaller solid cones, each of radius $3.5 \ cm$ and height $3 \ cm .$ find the number of cones so formed. $($Use $\pi=\frac{22}{7})$
View full solution →Two cubes, each of side $4 \ cm$ are joined end to end. Find the surface area of the resulting cuboid.
View full solution →A solid piece of metal in the form of a cuboid of dimensions $11 \ cm \times 7 \ cm \times 7 \ cm$ is melted to form $n$ number of solid spheres of radii $\frac{7}{2} \ cm$ each. Find the value of $n$.
View full solution →From a solid right circular cylinder of height $14 \ cm$ and base radius $6 \ cm ,$ a right circular cone of same height and same base radius is removed. Find the volume of the remaining solid.
View full solution →The dimensions of a solid iron cuboid are $4.4\ m \times 2.6 \ m \times 1.0\ m$. It is melted and recast into a hollow cylindrical pipe of $30 \ cm$ inner radius and thickness $5 \ cm$ . Find the length of the pipe.
View full solution →The $\frac{3}{4}$ th part of a conical vessel of internal radius $5 \ cm$ and height $24 \ cm$ is full of water. The water is emptied into a cylindrical vessel with internal radius $10 \ cm$ . Find the height of water in cylindrical vessel.
View full solution →The slant height of a frustum of a cone is $4 \ cm$ and the perimeters of its circular ends are $18 \ cm$ and $6 \ cm .$ Find the curved surface area of the frustum.
View full solution →In the figure below, a decorative block, made up of two solids $-$ a cube and a hemi $-$ sphere? The base of the block is a cube of side $6 \ cm$ and the hemisphere fixed on the top has a diameter of $3.5 \ cm$ . Find the total surface area of the block. $\text { (use } \left.\pi=\frac{22}{7}\right)$
View full solution →Water in a canal $, 5.4 \ m$ wide and $1.8\ m$ deep, is flowing with a speed of $25 \ \text{km / hour}$. How much area can it irrigate in $40$ minutes, if $10 \ cm$ of standing water is required for irrigation?
View full solution →A solid is in the shape of a right$-$circular cone surmounted on a hemisphere, the radius of each of them being $7 \ cm$ and the height of the cone is equal to its diameter. Find the volume of the solid.
View full solution →The boilers are used in thermal power plants to store water and then used to produce steam. One such boiler consists of a cylindrical part in middle and two hemispherical parts at its both ends. Length of the cylindrical part is $7 m$ and radius of cylindrical part is $\frac{7}{2} m$. Find the total surface area and the volume of the boiler. Also, find the ratio of the volume of cylindrical part to the volume of one hemispherical part.
View full solution →In a hospital, used water is collected in a cylindrical tank of diameter 2 m and height 5 m. After recycling, this water is used to irrigate a park of hospital whose length is 25 m and breadth is 20 m. If tank is filled completely then what will be the height of standing water used for irrigating the park. Write your views on recycling of water.
The height of a cone is 10 cm . The cone is divided into two parts using a plane parallel to its base at the middle of its height. Find the ratio of the volumes of the two parts.
In a rain-water harvesting system, the rain-water from a roof of $22 m \times 20 m$ drains into a cylindrical tank having diameter of base 2 m and height 3.5 m. If the tank is full, find the rainfall in cm. Write your views on water conservation.
View full solution →A 'circus' is a company of performers who put on shows of acrobats, clowns etc. to entertain people started around $250$ years back, in open fields, now generally performed in tents.
One such 'Circus Tent' is shown below.
The tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of cylindrical part are $9\ m$ and $30\ m$ respectively and height of conical part is $8\ m$ with same diameter as that of the cylindrical part, then find
$(1)$ The area of the canvas used in making the tent;
$(2)$ The cost of the canvas bought for the tent at the rate $Rs. 200\ \text{per} \ m^2, $ if $30 \ m^2$ canvas was wasted during stitching.
View full solution →One such 'Circus Tent' is shown below.
The tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of cylindrical part are $9\ m$ and $30\ m$ respectively and height of conical part is $8\ m$ with same diameter as that of the cylindrical part, then find
$(1)$ The area of the canvas used in making the tent;
$(2)$ The cost of the canvas bought for the tent at the rate $Rs. 200\ \text{per} \ m^2, $ if $30 \ m^2$ canvas was wasted during stitching.
A company deals in casting and moulding of metal on orders received from its clients.
The tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of cylindrical part are 9 m and 30 m respectively and height of conical part is 8 m with same diameter as that of the cylindrical part, then find
(1) The area of the canvas used in making the tent;
(2) The cost of the canvas bought for the tent at the rate Rs. 200 per sq. m, if 30 sq. m canvas was wasted during stitching.
The tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of cylindrical part are 9 m and 30 m respectively and height of conical part is 8 m with same diameter as that of the cylindrical part, then find
(1) The area of the canvas used in making the tent;
(2) The cost of the canvas bought for the tent at the rate Rs. 200 per sq. m, if 30 sq. m canvas was wasted during stitching.
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