In mean equation $\overline{ X }=a+\frac{\Sigma f i d i}{\Sigma f_i} d i$ _______ .
- ✓$x_i-a$
- B$a-x_i$
- C$f_i-a$
- D$a-f_i$
Answer: A.
View full solution →Question types
Surface Areas and Volumes question types
97 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
97
Questions
6
Question groups
5
Question types
01
M.C.Q (1 Marks)
43 Q→02Fill In The Blanks[1 Marks ]
7 Q→03True False[1 Marks ]
4 Q→042 Marks Questions
9 Q→053 Marks Question
19 Q→06Match The Following.
15 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.
The volume of a cube is $2744 \ cm ^3$. Its surface area is
- A$196 \ cm ^2$
- ✓$1176 \ cm ^2$
- C$784 \ cm ^2$
- D$588 \ cm ^2$
Answer: B.
View full solution →The ratio of the total surface area to the lateral surface area of a cylinder with base radius $80 cm$ and height $20 cm$ is
- A$1: 2$
- B$2: 1$
- C$3: 1$
- ✓$5: 1$
Answer: D.
View full solution →The height of a cylinder is $14 \ cm$ and its curved surface area is $264 \ cm ^2$. The volume of the cylinder is
- A$296 \ cm ^3$
- ✓$396 \ cm ^3$
- C$369 \ cm ^3$
- D$503 \ cm ^3$
Answer: B.
View full solution →The ratio of the volumes of two spheres is $8: 27$. The ratio between their surface areas is
- A$2: 3$
- B$4: 27$
- C$8: 9$
- ✓$4: 9$
Answer: D.
View full solution →$1 cm ^3=$ ........ $m l\left(1,10,10^2\right)$
View full solution →$1 m ^3=$ ........ $cm ^3 \cdot\left(10,10^3, 10^6\right)$
View full solution →1000 litres $=$ ........ cubic metre. $\left(1,10, \frac{1}{2}\right)$
View full solution →1 litre $=$ ........ cubic centimeter. $(1,100,1000)$
View full solution →The perimeter of the base of the hemisphere is $2 \pi$ then its volume is $cm ^3 ........ \left(\frac{\pi}{3}, \frac{3 \pi}{2}, \frac{2 \pi}{3}\right)$
View full solution →The curved surface area of the hemisphere is $2 \pi r^2$.
View full solution →The volume of the cylinder is $\frac{1}{2} \pi r^2 h$
View full solution →The volume of the rod having diameter $1 cm$ and length $8 cm$ is $2 \pi cm ^3$.
View full solution →The total surface area of the cylinder is $2 \pi r h$.
View full solution →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 →$($Use $\pi = 3.14)$
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 | B | |
| $Q.1.$ Area of minor sector | $(a)$ | $\pi r$ |
| $Q.2.$ Circumference of semi circle | $(b)$ | $\frac{\pi r^2 \theta}{360}$ |
| $(c)$ | $\frac{\pi r^2 \theta}{180}$ | |
| A | B | |
| $Q.1. CSA$ of cylinder $+\ CSA$ of hemisphere | $(a)$ | $\pi r^2 h$ |
| $Q.2.$ Volume of cone | $(b)$ | $\frac{1}{3} \pi r^2 h$ |
| $(c)$ | $2 \pi r(h+r)$ | |
| A | B | |
| $Q.1.$ volume of $10$ rupees coin | $(a)$ | $4 \pi r^2$ |
| $Q.2.$ Total surface area of hemisphere | $(b)$ | $\pi r^2 h$ |
| $(c)$ | $3 \pi r^2$ | |
| $A$ | $B$ | |
| $Q.1.$ Area of a minor sector | $(a)$ | $\frac{\pi r \theta}{180}$ |
| $Q.2.$ Circumference of circle | $(b)$ | $2 \pi r$ |
| $(c)$ | $\frac{\pi r^2 \theta}{360}$ | |
| A | B | |
| $Q.1.$ Total surface are a of cylinder | $(a)$ | $\pi r^2 h$ |
| $Q.2.$ Volume of cone | $(b)$ | $\frac{1}{3} \pi r^2 h$ |
| $(c)$ | $2 \pi r(h+r)$ | |
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