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Questions

1 / 10

Time

Score

Calculate the volumes

Use integration to find the volume of Rectangular Pyramid where l = 3m,
w = 3m and h = 3m

2 m³

9 m³

4 m³

Find the volume of a solid whose base is bounded by y=x³, x=2m, and the x-axis, and whose cross sections are perpendicular to the y-axis and are isosceles right triangles with a leg on the base of the solid

1.6 m3

3.4 m³

6.7 m³

Set up the integral to find the volume of solid whose base is bounded by the circle x²+y²=9, with perpendicular cross sections that are equilateral triangles.

$\int_0^{pi}\left(9+x\right)dx$

$\int_0^{3pi}\left(9-x\right)dx$

$\sqrt{3}$ $\int_{-3}^3\left(9-x^2\right)dx$

Use integration to find the volume of solid sphere with radius r=3m

6π m³

36 m³

36 π m³

Use integration to find the volume of a solid cylinder, r = 2m, h = 1m.
28.2 m³

28.2 m³

45.6 m³

56.3 m³

Use integration to find the volume of Rectangular Pyramid where l = Length of the base, w = Width of base and h = Height (base to tip)

(1⁄3) × l × w × h

(1⁄2) × l × w × h

(1⁄4) × l × w × h

Find the volume of a solid cylinder, r = Radius of the circular base, h = Height

πr²

πr²h

r²h

Use integration to find the volume of solid sphere with radius r

$\frac{4}{3}$ π r3

4πr³

3πr3

Set up the integral to find the volume of solid whose base is bounded by the graph of f(x) = $\sqrt{\sin x}$ , x=0 ,x=π, and the x-axis, with perpendicular cross sections that are squares.

$\int_0^{pi}\sin xdx$

$\int_0^{3pi}\sqrt{\sin x\ }dx$

$\int_0^{2pi}\sqrt{\sin x\ }dx$

Find the volume of solid whose base is bounded by the graph of f(x)= $\sqrt{\sin x}$ ,x=0,x=π, and the x-axis, with perpendicular cross sections that are squares

2 m³

3 m³

4 m³

Questions

Time

Score

Calculate the volumes

Use integration to find the volume of Rectangular Pyramid where l = 3m,w = 3m and h = 3m

2 m3

9 m3

4 m3

Find the volume of a solid whose base is bounded by y=x3, x=2m, and the x-axis, and whose cross sections are perpendicular to the y-axis and are isosceles right triangles with a leg on the base of the solid

1.6 m3

3.4 m3

6.7 m3

Set up the integral to find the volume of solid whose base is bounded by the circle x2+y2=9, with perpendicular cross sections that are equilateral triangles.

﻿∫0pi(9+x)dx\int_0^{pi}\left(9+x\right)dx∫0pi​(9+x)dx﻿

﻿∫03pi(9−x)dx\int_0^{3pi}\left(9-x\right)dx∫03pi​(9−x)dx﻿

﻿3\sqrt{3}3​﻿ ﻿﻿∫−33(9−x2)dx\int_{-3}^3\left(9-x^2\right)dx∫−33​(9−x2)dx﻿

Use integration to find the volume of solid sphere with radius r=3m

6π m3

36 m3

36 π m3

Use integration to find the volume of a solid cylinder, r = 2m, h = 1m.28.2 m3

28.2 m3

45.6 m3

56.3 m3

Use integration to find the volume of Rectangular Pyramid where l = Length of the base, w = Width of base and h = Height (base to tip)

(1⁄3) × l × w × h

(1⁄2) × l × w × h

(1⁄4) × l × w × h

Find the volume of a solid cylinder, r = Radius of the circular base, h = Height

πr2

πr2h

r2h

Use integration to find the volume of solid sphere with radius r

﻿43\frac{4}{3}34​﻿ π r3

4πr3

3πr3

Set up the integral to find the volume of solid whose base is bounded by the graph of f(x) = ﻿sin⁡x\sqrt{\sin x}sinx​﻿ , x=0 ,x=π, and the x-axis, with perpendicular cross sections that are squares.

﻿∫0pisin⁡xdx\int_0^{pi}\sin xdx∫0pi​sinxdx﻿

﻿∫03pisin⁡x dx\int_0^{3pi}\sqrt{\sin x\ }dx∫03pi​sinx ​dx﻿

﻿∫02pisin⁡x dx\int_0^{2pi}\sqrt{\sin x\ }dx∫02pi​sinx ​dx﻿

Find the volume of solid whose base is bounded by the graph of f(x)=﻿sin⁡x\sqrt{\sin x}sinx​﻿ ,x=0,x=π, and the x-axis, with perpendicular cross sections that are squares

2 m3

3 m3

4 m3

Incorrect

Great!

Use integration to find the volume of Rectangular Pyramid where l = 3m,
w = 3m and h = 3m

2 m³

9 m³

4 m³

Find the volume of a solid whose base is bounded by y=x³, x=2m, and the x-axis, and whose cross sections are perpendicular to the y-axis and are isosceles right triangles with a leg on the base of the solid

3.4 m³

6.7 m³

Set up the integral to find the volume of solid whose base is bounded by the circle x²+y²=9, with perpendicular cross sections that are equilateral triangles.

$\int_0^{pi}\left(9+x\right)dx$

$\int_0^{3pi}\left(9-x\right)dx$

$\sqrt{3}$ $\int_{-3}^3\left(9-x^2\right)dx$

6π m³

36 m³

36 π m³

Use integration to find the volume of a solid cylinder, r = 2m, h = 1m.
28.2 m³

28.2 m³

45.6 m³

56.3 m³

πr²

πr²h

r²h

$\frac{4}{3}$ π r3

4πr³

Set up the integral to find the volume of solid whose base is bounded by the graph of f(x) = $\sqrt{\sin x}$ , x=0 ,x=π, and the x-axis, with perpendicular cross sections that are squares.

$\int_0^{pi}\sin xdx$

$\int_0^{3pi}\sqrt{\sin x\ }dx$

$\int_0^{2pi}\sqrt{\sin x\ }dx$

Find the volume of solid whose base is bounded by the graph of f(x)= $\sqrt{\sin x}$ ,x=0,x=π, and the x-axis, with perpendicular cross sections that are squares

2 m³

3 m³

4 m³