Mensuration: Surface Area and Volume

A gift box in the shape of a cube has an edge length of $10$ cm. What is the total surface area of the box?

If the volume of a cube is $512 \text{ cm}^3$, find its total surface area.

What is the ratio of the volume of a cube of side $r$ to the volume of a cuboid of dimensions $r \times r \times 2r$?

The total surface area of a cube is $150 \text{ cm}^2$. What is its volume?

A water tank is a cuboid of dimensions $5$ m $\times$ $4$ m $\times$ $3$ m. If the internal surface of the tank (excluding the top lid) is to be cemented at a rate of Rs $50$ per square metre, find the total cost of cementing.

An iron beam is in the shape of a cuboid with dimensions as shown in the table below. If the density of iron is $8$ g/cm$^3$, find the mass of the beam in kilograms.

Find the side of a cube whose total surface area is equal to the surface area of a cuboid of dimensions $8 \text{ cm} \times 4 \text{ cm} \times 2 \text{ cm}$.

A classroom is $10\text{ m}$ long, $6\text{ m}$ wide and $5\text{ m}$ high. It has one door of dimensions $2\text{ m} \times 1\text{ m}$ and two windows of $1.5\text{ m} \times 1\text{ m}$ each. Find the cost of distempering the walls at Rs $15$ per square meter.

If the length of each edge of a cube is increased by $50\%$, what is the percentage increase in its total surface area?

A river $3\text{ m}$ deep and $40\text{ m}$ wide is flowing at the rate of $2\text{ km}$ per hour. How much water (in liters) will fall into the sea in one minute?

Find the lateral surface area of a cylinder of base radius $14$ cm and height $10$ cm. (Use $\pi = \frac{22}{7}$)

The volume of a cylinder is $3850$ cm$^3$ and its height is $25$ cm. Find its radius. (Use $\pi = \frac{22}{7}$)

If the curved surface area of a cylinder is $94.2$ cm$^2$ and its height is $5$ cm, find its radius. (Use $\pi = 3.14$)

What is the volume of a cylinder if its radius is $3.5$ cm and its height is $12$ cm? (Use $\pi = \frac{22}{7}$)

A cylindrical tank is open at the top. The radius is $3.5$ m and the height is $10$ m. Find the total surface area to be plastered on the inside (CSA + base).

Find the total surface area of a hollow cylinder with inner radius $r$, outer radius $R$ and height $h$.

A cylindrical tube, open at both ends, is made of metal $1$ cm thick. The outer radius is $11$ cm and length is $42$ cm. Find the volume of metal used. (Use $\pi = \frac{22}{7}$)

A cylindrical tub of radius $12$ cm contains water to a depth of $20$ cm. A spherical iron ball is dropped into the tub and the level of water rises by $6.75$ cm. What is the radius of the ball?

The curved surface area of a cylinder is $4400$ cm$^2$ and the circumference of its base is $110$ cm. Find the volume of the cylinder.

A cylindrical jar of radius $6$ cm contains oil. Iron spheres each of radius $1.5$ cm are immersed in the oil. How many spheres are necessary to raise the level of oil by $2$ cm?

The ratio of the radii of two cones is $1:2$ and the ratio of their heights is $2:1$. Find the ratio of their volumes.

Find the capacity in liters of a conical vessel with radius $7\text{ cm}$ and slant height $25\text{ cm}$. (Note: $1000\text{ cm}^3 = 1\text{ liter}$)

The volume of a cone is $1570\text{ cm}^3$. If its base area is $314\text{ cm}^2$, find its vertical height.

If the slant height of a cone is $21\text{ m}$ and the diameter of its base is $24\text{ m}$, find its total surface area.

A cone and a cylinder have the same height. If the radius of the cone is twice that of the cylinder, what is the ratio of the volume of the cone to the volume of the cylinder?

If the slant height of a cone is increased by $10\%$ and the radius is decreased by $10\%$, what is the percentage change in its curved surface area?

How many meters of cloth $5\text{ m}$ wide will be required to make a conical tent, the radius of whose base is $7\text{ m}$ and height is $24\text{ m}$?

The area of the base of a cone is $616$ cm$^2$ and its slant height is $25$ cm. Find the volume of the cone. (Use $\pi = \frac{22}{7}$)

A right circular cone has a volume of $1232$ cm$^3$ and height $24$ cm. Find the radius of its base. (Use $\pi = \frac{22}{7}$)

The total surface area of a cone is $704$ cm$^2$ and the radius of its base is $7$ cm. Find the slant height of the cone. (Use $\pi = \frac{22}{7}$)

If the volume of a sphere is numerically equal to its surface area, what is its radius?

A shot-put is a metallic sphere of radius $4.9$ cm. If the density of the metal is $7.8\text{ g/cm}^3$, find the mass of the shot-put (approx).

Find the ratio of the surface area of a sphere of radius $r$ to its volume.

A hemispherical tank is full of water. If the volume of water is $2425.5\text{ cm}^3$, find its radius. (Take $\pi = \frac{22}{7}$)

Find the volume of a sphere whose surface area is $154\text{ cm}^2$. (Take $\pi = \frac{22}{7}$)

The diameter of a sphere is reduced by $25\%$. By what percentage does its surface area decrease?

A hemispherical bowl has a radius of $3.5$ cm. What would be the volume of water it would contain? (Take $\pi = \frac{22}{7}$)

Find the volume of a sphere whose surface area is $154$ cm$^2$.

Twenty-seven solid iron spheres, each of radius $r$ and surface area $S$ are melted to form a sphere with surface area $S'$. Find the radius $r'$ of the new sphere.

A capsule of medicine is in the shape of a sphere of diameter $3.5$ mm. How much medicine (in mm$^3$) is needed to fill this capsule?

The perimeter of the base of a square pyramid is $24\text{ cm}$ and its height is $4\text{ cm}$. Find its volume.

A square pyramid has a volume of $48\text{ cm}^3$ and a height of $9\text{ cm}$. Find the side length of the base.

What is the volume of a right pyramid if its base is a square of side $x$ and its height is $x$?

A pyramid has a hexagonal base with area $50\text{ cm}^2$ and height $12\text{ cm}$. Calculate its volume.

If the side of the base of a square pyramid is doubled and the height is halved, what happens to the volume?

Find the total surface area of a regular triangular pyramid (tetrahedron) where each edge is $6\text{ cm}$. (Area of equilateral triangle = $\frac{\sqrt{3}}{4}s^2$)

A square pyramid has a base area of $144\text{ cm}^2$ and a volume of $480\text{ cm}^3$. Find its slant height.

A trophy designer is creating a custom awards piece in the shape of a right square pyramid. The base of the pyramid has a side length of $10\text{ cm}$. The total surface area of the pyramid, including the base, is $360\text{ cm}^2$. The designer needs to calculate the volume of the pyramid to determine the amount of resin required for casting. Given these dimensions, what is the volume of the trophy in cubic centimeters? (Take $\sqrt{11} \approx 3.32$ if necessary)

A right square pyramid has a volume of $1280$ cm$^3$ and its vertical height is $15$ cm. Find the slant height of the pyramid.

A solid pyramid has a square base with diagonal $10\sqrt{2}$ cm. If its slant height is $13$ cm, find the total surface area of the pyramid.